Program Sampler
A whole new teaching equation
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Suggested Teaching Sequence 1
2
5
Plan
Differentiated Group Work
Teacher Resource Book
Activity Zone
• Plan and pre-assess using resources in the topic-based booklet from the Teacher Resource Box.
• Small group work with students who may need further instruction while the rest of the class works in groups on differentiated learning centre activities from the Activity Zone, recording their work in their Maths Thinking Skills Book.
Introduce
(This group work may include digital activities using the Tools4Maths)
Teacher Resource Book
• Differentiated worksheets (from the Teacher Resource CD) used for extra fluency practice at home or school.
• Introduce each lesson by setting the purpose and make connections to students’ previous learning • Whole class teaching focus consolidating the concept and including problem solving (incorporating use of concrete materials)
6
Reflection Maths Thinking Skills Book
3
• Whole-class reflection. Students record reflections in Maths Thinking Skills Book.
Conceptual Understanding Interactive Whiteboard DVD • Explore the concept through watching the Visual Learning Animation and the Visual Learning Bridge (topic-opener videos in Tears 5 and 6).
4
7
Assessment • Ongoing and throughout using observations and recorded work in Maths Thinking Skills Book and topic-based pre- and post-assessment using forms from teacher booklet. Includes assessment of reasoning.
Guided and Independent Practice Student Activity Book • Students complete activities in Student Activity Book
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Program Sampler AUSTRALIAN
CURRICULUM
A whole new teaching equation Introduction This sampler from enVisionMATHS Year 4 demonstrates the suggested teaching sequence using sample pages from the different Year 4 components. This is representative of the components across Years 3 to 6. There are some minor differences between these and the components for Years F to 2, but the suggested teaching sequence is the same.
Year 4 Topics The enVisionMATHS program is organised around 12 to 13 Topics per year level. All components are connected to the topics.
Contents Suggested Teaching Sequence
2
Contents, Introduction and Year 4 Topics list
3
Year 4 Topic 2 Teacher planning pages
4
Year 4 Topic 2 Topic opener page from Student Activity Book
10
Year 4 Topic 2 Samples of lesson pages in Teacher Booklet (from Teacher Resource Box 4)
12
Year 4 Topic 2 Sample of Visual Learning Bridge, Animation and Tools4Maths
18
Year 4 Topic 2 Lessons 2.1, 2.2, 2.3 Student Activity Book pages
20
Year 4 Topic 2 Activity Zone Cards
26
Maths Thinking Skills Book 3 to 6 sample pages
34
Year 4 Topic 2 Lessons 2.1, 2.2, 2.3 Differentiated worksheets (from Teacher Resource CD in Teacher Resource Box 4)
45
Year 4 Topic 2 Samples of Pre- and Post-assessment pages in Teacher Booklet and Teacher Resource CD (from Teacher Resource Box 4)
54
Components Chart
60
Addition Concepts and Strategies
Topic
2
Looking Back
✪ Year 3 Lessons
Year 4
Topic 2: Addition Concepts and Strategies
✪ Topic 2 Lessons
2.1 Using Mental Maths to Add
2.2 Adding Tens to a 2-Digit Number
2.3 Adding Whole Numbers
2.4 Adding Tens and Ones
2.4 Adding Three or More Numbers
2.5 Using Models to Add
2.5 Using Diagrams to Connect Addition and Subtraction
Looking Ahead
✪ Year 5 Lessons
Topic 2: Addition and Subtraction Mental Strategies 2.1 Using Mental Maths to Find Missing Parts
2.2 Rounding and Estimating Whole Numbers
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2.1 Using Mental Maths to Make Ten
2.2 Using Models to Add 3-Digit Numbers
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Skills Trace
2.7 Adding Larger Numbers
2.3 Using Mental Strategies to Add and Subtract
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Suggested Teaching Sequence
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2.4 Adding and Subtracting Large Numbers
Topic • Teacher planning (using pages 2–11 of this booklet)
Note Blue text = suggested question/language for teachers to use
• Use Topic Opener to introduce topic (page 2)
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Pink text = answer/solution
• Pre-assessment given to students (pages 23–26)
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Lessons • Introduce each lesson by setting the purpose
• Make connections to students’ previous learning (connect) • Watch the Visual Learning Animation (VLA) and show students the Visual Learning Bridge (VLB) on the IWB or at the top of the relevant lesson page in the Student Activity Book
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• Whole-class teaching focus consolidating the concept and including problem solving
• Students complete activities in the Student Activity Book • Small-group work with students who may need further instruction (error intervention, extension); rest of class work in groups on differentiated learning centre activities from the Activity Zone that are appropriate to their level (refer to pages 8–11 of this booklet), recording their findings in the Maths Thinking Skills Book • Whole-class reflection • Students record their reflections in the Maths Thinking Skills Book
• Differentiated worksheets used for extra practice at home or school
Assessment • Ongoing and throughout using pages 22–30, including post-assessment (pages 27–30), observations and recorded work in the Maths Thinking Skills Book
4
Year 4 Topic 2 Teacher planning pages
Contents
Topic
2
Planning
2
Maths Background for Teachers
2 4
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Maths Language Meeting Individual Needs
5
enVision Minds
6
enVision Investigations
7
enVision Games
8
enVision Digital
10
11
Lessons 2.1 Using Mental Maths to Add 2.2 Using Models to Add 3-digit Numbers 2.3 Adding Whole Numbers
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2.4 Adding Three or More Numbers
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enVision Reflection
12 14 16 18
2.5 Using Diagrams to Connect Addition and Subtraction
20
Review and Assessment
22 22
Pre-assessment Concepts 1–4
23
Post-assessment Concepts 1–4
27
Assessment Answers
31
Sources
32
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Overview of Assessment
Strand Colours
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Number and Algebra Measurement and Geometry Statistics and Probability written by
Rochelle Manners
with Carmen Morgan • Matt Skoss
5
Maths Background for Teachers
• There are multiple interpretations of addition, subtraction, multiplication and division of rational numbers, and each operation is related to other operations. • There is more than one algorithm for each of the operations with rational numbers. Most algorithms for operations with rational numbers, using both mental maths and paper and pencil, use equivalence to transform calculations into simpler ones.
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2.4 Three or more whole numbers can be grouped and added in any order.
Topic Focus
2.5 Addition and subtraction have an inverse relationship. The inverse relationship between addition and subtraction can be used to find subtraction facts—every subtraction fact has a related addition fact.
Australian Curriculum Links Number and Algebra
Essential Understandings
• Number and place value
NA073 Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems 2.1–2.4
• Patterns and algebra
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2.2 Models and standard algorithms for adding 3-digit numbers are just an extension to the hundreds place of the models and standard algorithms for adding 2-digit numbers.2.3 The standard addition algorithm for multi-digit numbers breaks the calculation into simpler calculations using place value, starting with the ones, then the tens and so on.
NA055 Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation 2.5
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2.1 There is more than one way to do a mental calculation. Techniques for doing addition mentally involve changing the numbers of the expression so the calculation is easier to do mentally and has the same answer as the original calculation.
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NA083 Use equivalent number sentences involving addition and subtraction to find unknown quantities 2.5
About Addition Concepts and Strategies Topic Opener
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Introduce students to the topic of addition concepts and strategies by focusing on the thought-provoking real-life questions and vocabulary used in the Topic Opener. Encourage students to come up with their own questions. Model the vocabulary listed in the Topic Opener and ensure students understand the terms.
2 Topic 2 ✪ Addition Concepts and Strategies Maths Background for Teachers
6
Year 4 Topic 2 Teacher planning pages
Estimation
What is mental maths? Mental maths is the process of finding an exact answer to a calculation in your head. Mental maths is also used to find an estimated answer. Many mental maths techniques for addition rely on the ability to decompose or break apart numbers in a way that is appropriate to the situation. Partitioning into place values involves breaking apart one or both numbers into expanded form. Then the ‘parts’ are rearranged to create a set of additions that are each simpler than the original addition.
Why estimate? When you estimate a sum, you determine about how much it is. Students should be encouraged to estimate sums before calculating. This practice helps them keep in mind an approximate number that the answer may be. Then after they have performed the calculation, they can look back to check if the answer is reasonable. As students proceed in their study of mathematics, they will learn about some situations where an estimate is sufficient.
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Using Mental Maths
Always distinguish between estimates and exact answers when discussing calculations with students. For example, if 427 1 291 is estimated as 400 1 300, refer to that sum as ‘about 700’.
Partitioning one addend into place values 51 28 = 51 (20 8) = (51 20) 8
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Using Models
= 71 8
A diagram can be used to represent addition of whole numbers. A labourer earned $50 at his first job and $35 at his second. What did he earn in total? [$85]
= 79 Partitioning two addends into place values 51 28
Initial amount $50
= (50 20) (1 8) = 70 9
Amount added: $35
$50 $35 $85
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= (50 1) (20 8)
Give counters to students who are having trouble with addition to model the problems.
= 79
76 15 = 76 (4 11)
Numerical equivalence
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Bridging tens is another technique. To use this technique, first identify the amount needed to count on from one number to the next multiple of 10. Then use that amount to partition the other number.
= (76 4) 11 Associative property of addition Addition
= 91
Addition
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= 80 11
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These techniques for mental maths are rooted in the properties of numbers and operations. For example, when 15 is replaced by an expression such as 4 11, it is an application of numerical equivalence. That is, a number can be named in different ways without changing its value. The justification for other steps varies from calculation to calculation.
Topic 2 ✪ Addition Concepts and Strategies Maths Background for Teachers 3
7
Maths Language Vocabulary
ESL
Language of Addition Concepts and Strategies
Considerations for ESL Students
Review Vocabulary
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Help students become familiar with Topic 2 terms as they relate to addition concepts and strategies. The following terms will all be encountered in this topic.
Repeated oral-language practice of the terms that describe mental computations will help English learners remember and understand the steps.
New Vocabulary
hundreds digit
sum
ones digit
estimate
• Beginning Review with special needs students how to use an estimate to help check their answer to an addition problem.
tens digit
Making real-life connections to vocabulary can strengthen students’ understanding of mathematical terms.
Partitioning strategy
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This strategy works well for addition with or without regrouping. Students should first separate each number into its place value. Starting with the greatest place value, add the sums for each place value.
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When I partition something, it is now two or more smaller parts. I can put these back together to make the whole thing.
Vocabulary Activities
Identifying something apart, it is now two or more smaller parts. I can put these back together to make the whole thing.
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Draw a sum on the board and have students identify the answer. Give them three more problems and ask them to estimate the answer and then calculate the sum. Have them describe in a sentence. For example: ‘The estimate to this question was four but the answer was five.’
48 + 26 = ?
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Partitioning strategy 40 + 20 60
8 + 6 14
60 + 14 74
Regrouping 50 + 26 76 – 2 74
4 Topic 2 ✪ Addition Concepts and Strategies Maths Language
8
• Intermediate Be sure these students estimate first for every problem. If their answer is not near the estimate, they should check their work.
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Connection to Everyday Vocabulary
• Advanced Have students compare their estimates with the actual sums and comment on whether or not their estimations are correct (that is, identify whether they are estimating correctly or not).
ESL Activity: Listen Up! Use with Lesson 2.4 10–15 minutes 5 min
10 min
15 min
• Some students may have trouble accurately copying large numbers. Write the following numbers on the board in vertical form: 38 451, 146 233; and 34 098, 190 436. • Group students in pairs with one student reading the first number aloud while their partner copies the number onto paper. When dictating the numbers, students should say each digit rather than reading the word form. For example, 38 451 is dictated as ‘three, eight, four, five, one’. • Have partners swap roles to copy the second number onto paper.
Year 4 Topic 2 Teacher planning pages
Meeting Individual Needs Emerging-level
Extending-level
Considerations for Additional Needs Students
Considerations for Emerging-level Students
Considerations for Extending-level Students
• Additional needs students will benefit from visual models that illustrate how 2-digit numbers can be broken apart and combined in many ways.
• Pairs of students may benefit from using words to write addition sentences. One partner writes a sentence and the other partner writes the symbols to complete the sentence.
• Challenge students to use logic and reasoning skills to estimate sums. Have them track the variety of ways in which they are able to solve problems without using a paper-and-pencil method.
Emerging-level Activity: Original Story Problems
• Connect students who have a firm grasp on the paper-and-pencil addition algorithm with the concept of multiplication. Allow them to explore the idea that adding doubles is the same as multiplying by two and so on.
10–15 minutes 5 min
Additional Needs Activity: Comparing Numbers
15 min
• Instruct partners to each write a joining, separating or comparing story problem involving two characters and the number of books in their bookcases. For example, one character can give the other books, one character can take away some books, or one character can have more books than the other.
• Have partners exchange problems and solve with both a drawing and a number sentence. If time allows, ask partners to try to modify their story problems so that the necessary operation is now addition or subtraction.
Use with Lesson 2.1
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10–15 minutes 10 min 15 min Materials number cards 0–9 place-value blocks
Mark has 7 books in his bookcase. His mother gives him 3 more. How many books does Mark have altogether? 7 + 3 = 10
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5 min
10 min
• Have students shuffle the number cards and place them face down in a stack.
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• The first student draws two cards and forms a 2-digit number. The second student uses place-value blocks to model the number.
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• The third student draws two more cards and forms another 2-digit number. The fourth student uses place-value blocks to model the number.
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• Students then combine all the tens blocks and find the sum. Then they combine the ones blocks and find the sum.
Extending-level Activity: 3-Digit Numbers Use with Lesson 2.2
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• Write 18 46 on the board. Have students display place-value blocks for each number. Move two ones blocks from the model of 46 to the model of 18. Exchange the 10 ones blocks for one tens block. Ask students to name the addition sentence the blocks now model and find its sum. [20 44 64]
Use with Lesson 2.5
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• Write 36 23 on the board. Display placevalue blocks for each number. Group all the tens blocks together and have students find the sum. Group all the ones blocks together and have students find the sum. Add the sums together to find the total sum of the blocks.
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Additional Needs
Mark has 7 books in his bookcase. His mother has 3 in her bookcase. How many more books does Mark have? 7–3=4
5 min
10 min
10–15 minutes 15 min
• Ask students to take turns doing these steps. • Write any 3-digit number with two in the hundreds place. • Write any 3-digit number with four in the hundreds place. • Write a third number so that the sum of all three numbers will be between 900 and 1 000. • Add to verify that the sum is between 900 and 1 000. Students can work together to adjust the third number. • As an extension, ask students to determine the range of 3-digit numbers that would work given the selection of the first two numbers.
• Have each pair write a set of steps for another, similar problem.
• Students can write and solve a new addition sentence modelled by the blocks.
4
5
1
7
40 + 10 = 50 5 + 7 = 12 50 + 12 = 62 Topic 2 ✪ Addition Concepts and Strategies Meeting Individual Needs 5
9
Topic
2
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Construction of the Sydney Harbour Bridge was completed in 1932. The Sydney Opera House was completed in 1973. Use mental maths to estimate how many years there were between the completion of each of these famous Australian landmarks.
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Addition Concepts and Strategies
12
twelve
10
Year 4 Topic 2 Topic opener page from Student Activity Book
Vocabulary
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During the 2009 Ashes cricket series, in the second test match at Lord’s, Australia scored 215 runs in the first innings and 388 in the second innings. How many runs did they score for the match?
bridging partitioning splitting regrouping place-value blocks whole numbers sum fact family
m
k 20
km
Brisbane
2690 km
960
This map of Australia shows the driving distances between some Australian cities. How many kilometres is it to drive from Perth to Melbourne, via Adelaide?
Alice Springs 30
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Darwin
Perth Adelaide
72
5k
Sydney km 285 km Canberra 660 km
m 875
Melbourne
Hobart
thirteen
11
13
Using Mental Maths to Add
Topic
2
Lesson
1
Student Activity Book pages
Prevent Misconceptions
Using Mental Maths to Add
1
Understand it!
Visual Learning Bridge (VLB)
Dr Pickford recorded how many whales, dolphins and seals she saw. How many whales did she see during the two weeks?
Numbers can be broken apart to find sums using mental maths.
6 �
Week� Week
Week�� Week
Whales
25
14
Dolphins
28
17
Seals
34
18
�
50 42
��
43 3
46 �
4
71 13
84
�5
52 44
96 �
6
54 7
6
25 14 25 5 9 30 9 39
25 14 (20 10) (5 4) 30 9 39
Dr Pickford saw 39 whales.
Dr Pickford saw 39 whales.
Use partitioning to add mentally. �� 72 18 (70�+�0)�+�(���+�8)
�� 34 25
(�0�+��0)�+�(4�+�5)
80�+�0
50�+�9
90
59
Guided Practice
Use bridging the tens to add mentally.
Bridge the tens.
0 ) (5 2) 7
37 Reasoning
8
�4 47 9 47�+���+�6
�8
�0 46 23 (40 20) (
6
69
60�+���
56
9�
Problem Solving � 6a�I bought a T-shirt for $26 and a pair of shorts for $27. Use mental maths to find the total cost of the two items.
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� How does knowing that 17 2 15 help you to find 28 17 mentally?
� b�How many different ways can you solve this problem? Explain your thinking.
Answers�will�vary.�You�can�bridge�the�tens�by�adding���to��8� bridge the tens by adding���to��8
Answers�will�vary.�
to�make��0,�and�then�add�the�5�to�make�45. 5 to make 45.
For�example,�you�can�bridge�the�tens�(�6�+�4�+����=��0�+����=�5�)�
or
or�use�partitioning�(�0�+��0�+�6�+�7�=�40�+���=�5�).
4�� �� fourteen
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�5 55 37 55�+�5�+���
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3)
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30
4
30 8
�4
64 Use partitioning. 25 12 (20
26 12 26
ed
8
38 26 38 2 24 40
�9
Using partitioning by splitting the numbers. Add the tens. Add the ones.
Independent Practice
9�
�7
25 14
Bridging the tens by adding 5 more to make 30.
Animal
Mental Computation
Another way
25 14
Marine�Animals�Seen Marine Animals Seen
Find 25 14.
� � 35 26
One way
How�can�you�add�with�mental�maths?
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Lesson
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2
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Could you separate 14 to 7 7 instead of 10 4? [Yes.] Would it help the calculations? [No, as it wouldn’t make the calculation as easy as using tens.]
What does it mean to add with mental maths? [Sample response: It means to find the answer in your head.]
Topic
Students may not understand that partitioning numbers involves two or three additions to do the one sum. Remind students that adding using mental maths uses a series of steps. To help students keep track of steps, have them use sequence words such as first, next, last.
fifteen ��5 5
Curriculum link: NA073
Problem Solving
16a The total cost of the two items is $53.
b How many ways did students think of? Ask students to share their strategies to see how many different ways the class has thought of. Are some better than others? Do students now see a better way of thinking? Make 10 to add mentally
26 4 30
30 the remaining 23 53
Partitioning
20 20 40
6 7 13
40 13 53
26 and 27 are near doubles Double 26 is 52 52 1 53 OR Double 27 is 54
12 Topic 2 ✪ Addition Concepts and Strategies
Using Mental Maths to Add
12
54 1 53
Year 4 Topic 2 Samples of lesson pages in Teacher Booklet (from Teacher Resource Box 4)
Topic
2
Lesson
1
Explore the Concept
There are multiple interpretations of addition, subtraction, multiplication and division of rational numbers, and each operation is related to other operations.
Ask students to add 1 1; 2 2; 3 3 and other simple sums. Have them tell a partner the answers as quickly as possible. How did you come up with those answers so quickly? Now, what if you were asked to add 15 14, would that be easy still? Allow students to explore the concept, and if they do find it easy, give them harder problems to explore. Or if they find it difficult, make the questions as simple as possible to help them get started positively.
Quick and Easy Lesson Overview Objective Students solve problems by adding with mental maths.
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Topic Focus
Error Intervention
Essential Understanding There is more than one way to do a mental calculation. Techniques for doing addition mentally involve changing the numbers of the expression so the calculation is easier to do mentally and has the same answer as the original calculation.
Maths Background for Teachers Instruction in mental arithmetic can help students see that they can make problems easier to solve. In this lesson students learn about partitioning numbers into tens and ones as a technique they can use to simplify an addition problem and find the solution mentally.
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If students don’t know how to partition a number or where to start with each problem, demonstrate that there are multiple ways to partition numbers, none of which is better or worse, but different ways will suit different students. For example: In question eight, you use bridging the tens; however, you could just as easily use partitioning as in question nine. Once you are used to the questions, you can use whichever method you find suits you best.
Extension
Booker et al. (2010) describe a method of ‘thinking in tens’ to help students add numbers; so 40 30 70 is the same as 4 3 7. Methods like this and other mental applications that break down the calculations into methods that make it easier for students will be useful.
Set the Purpose
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Students may find it easier to compute with numbers in different ways. Note that the properties of addition of whole numbers can be used to justify the mental techniques students will use to get correct answers.
Have students work in pairs. Have one student use the ‘bridge the tens’ method and the other partner break apart by partitioning. Solve the problem 27 1 44. Which method is easiest? [Responses will vary.]
Small-group Interaction
Work with a small group who may need further instruction, practice or extension. Use blocks, counters and other concrete materials; review the VLA with students; make further connections to real life; or look at one of the Investigations together. Other students work in groups on learning centre activities from the Activity Zone (Minds, Investigations, Games and Digital activity cards, see pages 6–11 of this booklet). Students will record their findings in their Maths Thinking Skills Book. Give students a group quiz to mentally add the numbers as quickly as possible. Encourage the group to let each other have a turn.
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You know how to add numbers on a hundred chart. Today, you will add with mental maths by using place value or by making a ten.
Reflection
Connect
In this lesson you learnt different ways to partition numbers to solve addition problems using mental maths. In which two ways could you partition the sum 47 16? What does this mean in general?
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Describe a time when you needed to add something in your head. Encourage students’ responses.
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Differentiated Worksheets
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Provide spare paper and concrete materials such as counters to help students completing the Replay worksheet to model the additions. Encourage the students attempting the Challenge worksheet to explain their working and to check their answers. Review with students the partitioning principles for the Challenge activity.
Topic
2
Replay
Practice
Replay
Topic
Lesson
1
4
Name
2
1
Topic
4
Name
Using Mental Maths to Add
Using Mental Maths to Add
You can break apart numbers to make them easier to add mentally.
Bridge to tens to add mentally.
Add 31 1 45 by breaking apart numbers.
Add 26 1 17 by breaking apart numbers to make a ten.
Break the numbers into tens and ones.
Use a number that adds with the 6 in 26 to make a 10. Since 6 1 4 5 10, use 4.
tens
ones
31 5
30
1
1
45 5
40
1
5
Think: 17 5 4 1 13
Add the tens: 30 1 40 5 70
5 42 1
87
5 (20 1 20) 1 (7 1 5
4 25 1 49 5
5 37 1 56 5
79 93
3 54 1 23 5 6 77 1 13 5
5 47 1 40 1
4
5
5 71
5 88
71
B Think of 43 as 44 1.
1
C Think of 8 as 10 2.
87 1 1
5 62 1 9
5 54 1 12
Find each total using mental maths. 2 36 1 43 5
Name
A Think of 8 as 4 4.
3 47 1 41
20 1 9
So, 42 1 29 5
4 27 1 21
So, 31 1 45 5 76
95 74
1
Break It Up and Add
Explain.
Add 43 10 53, then subtract 2.
So, 47 1 41 5
88
Use the split strategy to add mentally.
Add the totals: 70 1 6 5 76
1 24 1 71 5
Challenge Lesson
43 8
51
2 Which choice helps the most to solve 67 29?
So, 26 1 17 5 43
Add the ones: 1 1 5 5 6
30 1 4 5 83 1 4
5 53 1
So, 53 1 34 5
Add: 30 1 13 5 43
2
1 Which choice helps the most to solve 43 8?
2 42 1 29
1 53 1 34
5 87
Add: 26 1 4 5 30
Challenge
Practice Lesson
77 90
7 To add 32 1 56, Chloe first added 30 1 50. What two steps does she still need to do to find the total? What is Chloe’s total?
She needs to add 2 1 6 5 8 and then 80 1 8 5 88.
3
So, 27 1 21 5
Steve can break apart 34 as 32 1 2, so he can make a ten by adding 48 1 2 5 50. Then he can add 50 1 32 5 82.
5 (50 1 10) 1 (4 1 5 60 1
5 48
13 )
54
5 50 1
5 66
48
5 (30 1
2 2
B Think of 29 as 30 1. ) 1 (8 1 1)
Add 67 30 97, then subtract 1.
5 59
So, 54 1 12 5
66
So, 38 1 21 5
8 47 1 8
78
55
11 43 1 38
12 72 1 7
81
79
C Think of 29 as 25 4. Explain.
59
67 29
96
3 Which choice does not help you solve 63 28 using mental maths? A Think of 63 as 60 3.
Find each total using mental maths. 7 52 1 26
8 How can Steve add 48 1 34 by making a ten? What is the total?
21)
18
A Think of 67 as 63 4.
6 38 1 21
9 32 1 17
10 28 1 31
49 13 42 1 33
59 14 36 1 14
75
50
15 Daniel broke apart a number into 30 1 7. What number did he start with?
37
B Think of 28 as 30 2. C Think of 28 as 25 3. Explain.
You should find the sum using tens. 25 is not a tens number. 91
63 28
16 What is the total of 27 1 42 using mental maths? A 68
B 69
C 78
D 79
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
Topic 2 ✪ Addition Concepts and Strategies
13
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
Using Mental Maths to Add 13
Topic
2
Lesson
Using Models to Add 3-Digit Numbers
2
Student Activity Book pages
2
Using Models to Add 3-Digit Numbers
Lesson
2
Understand it!
285
143 143
You can add whole numbers by using place value to break them apart.
285
285
1 hundred 1 hundred 2 hundreds 4 hundreds
Another Example
2 tens 8 ones
428
143 285 428
4 tens 8 tens 12 tens
12 tens 1 hundred 2 tens
Find 143 285.
4 hundreds
3 ones 5 ones 8 ones
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Visual Learning Bridge (VLB)
Some students may forget to regroup 10 or more tens as hundreds. Encourage students to estimate to see if their answers are correct.
143
How can you add 3-digit numbers with placevalue blocks?
Place-value blocks can model regroupings in addition problems with larger numbers.
Prevent Misconceptions
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Topic
Why don’t we need to regroup ones? [There are fewer than 10 ones, so we don’t need to regroup.] When you add four tens and eight tens you get 12 tens, what should you do with the 12 tens? [Regroup 12 tens as one hundred, two tens.]
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How do you use place value to break apart the number 143? [143 can be broken apart into one hundred, four tens, three ones.]
Regroup.
Add the hundreds.
Independent Practice
How do you add with two regroupings? Find 148 276 424
Write each problem and find the sum. 4
Step 1
Step 2
Step 3
Add the ones
Add the tens
Add the hundreds
5
1 hundred 1 hundred 2 hundreds 4 hundreds
202 318 520
ed
279 143 422 1 ten 4 tens 7 tens 12 tens
Regroup
Regroup
14 ones 1 ten 4 ones
12 tens 1 hundred 2 tens
Guided Practice 1
So, 148 276 424
ct
8 ones 6 ones 14 ones
Write the problem and find the sum.
7
337 152 489
Problem Solving 8a 8a I add two 3-digit numbers. The sum is a 4-digit number. How is this possible?
b b What is the largest total I could have? Explain how you know.
re or
635 222 857
then we regroup 10 hundreds to make 1 000. This is possible.
The largest total is 1 998. The largest possible two 3-digit numbers are 999 and 999, and their sum is 1 998.
3 138 29 167
seventeen 17 17
Curriculum link: NA073
U nc
16 sixteen
6
When the sum of the hundreds is more than 10 hundreds,
Use place-value blocks or draw pictures to find each sum. 2 256 162 418
134 158 292
Find each sum. Use place-value blocks or draw pictures to help.
Problem Solving
8a This is possible. When the sum of the hundreds is more than 10 (hundreds), then we regroup 10 hundreds to make 1 000. What is the largest number we could have in the thousands place in this situation? [The largest number is 1(1 000).] How can you explain this? Ask students to show examples to illustrate.
14 Topic 2 ✪ Addition Concepts and Strategies
b The largest total is 1 998. How many students were able to work this out using their knowledge of place value? The largest two 3-digit numbers are 999 1 999, which equals 2 000 2 2 5 1 998. Encourage this use of mental computation.
Using Models to Add 3-Digit Numbers
14
Year 4 Topic 2 Samples of lesson pages in Teacher Booklet (from Teacher Resource Box 4)
Topic
2
Lesson
2
Error Intervention
There is more than one algorithm for each of the operations with rational numbers. Most algorithms for operations with rational numbers, using both mental maths and paper and pencil, use equivalence to transform calculations into simpler ones.
If students mix up the hundreds, tens and ones places, then draw a place-value chart on the board and ask: How could we use this chart to write the addition problem? [Sample answer: Write the numbers one above the other in the chart. Put one digit in each column from left to right.] Write the numbers in the chart as shown below, then have students add each place value. They can use a picture or blocks to help them come up with an answer.
Quick and Easy Lesson Overview Objective Students add 3-digit numbers using place-value blocks or pictures and record the results using the standard addition algorithm. Essential Understanding Models and standard algorithms for adding 3-digit numbers are just an extension to the hundreds place of the models and standard algorithms for adding 2-digit numbers.
Hundreds
Tens
Ones
2
7
4
6
3
1 2 1 3 hundreds 7 6 13 tens 4 3 7 ones 13 tens is 1 hundred and 3 tens So the answer is 437.
eP
Vocabulary place-value blocks sum
ro of s
Topic Focus
whole numbers fact family
If students forget to use zero as a placeholder, remind them that if they regroup all the ones or all the tens, they must record a zero in the sum to indicate that nothing is left of the corresponding place. This activity could also be used to prevent confusion and misconceptions.
Place-value blocks help students understand addition by helping them see how to regroup. That is, when the total number of blocks in a given place is less than 10, students see that there is no need to regroup. When the total number is 10 or greater, they are able to see how regrouping becomes necessary. The physical process of performing the regrouping—trading 10 ones for one ten, or 10 tens for one hundred—reinforces the meaning of regrouping numbers that are written in columns when the traditional method is applied. Regrouping will also be useful to help students who are visual-spatial learners or kinaesthetic learners.
Pa g
Maths Background for Teachers
Extension
Have students work on the sum 158 162. Allow them time to complete the problem. In this problem, regrouping will happen twice—from ones to tens and tens to hundreds. Help students through the example if necessary. Give them further examples that require regrouping: 145 155; 344 469; 54 188.
Small-group Interaction
Set the Purpose
Work with a small group who may need further instruction, practice or extension. Use blocks, counters and other concrete materials; review the VLA with students; make further connections to real life; or look at one of the Investigations together. Other students work in groups on learning centre activities from the Activity Zone (Minds, Investigations, Games and Digital activity cards, see pages 6–11 of this booklet). Students will record their findings in their Maths Thinking Skills Book.
ed
In this lesson, you will use place-value blocks (or pictures) to add two 3-digit numbers and then record the result using paper and pencil.
Connect
ct
Describe a situation when you might need to add two 3-digit numbers. [Sample responses: Adding scores of a game such as bowling; adding the number of students in two grades in our school.]
Explore the Concept
or
re
Provide students with place-value blocks and, in pairs, have them create the same value using different-sized blocks. Give one student the ones and the hundreds, and give the other student the tens. Have them match the same amounts such as 30, and then 200.
Differentiated Worksheets
2
U nc
Provide spare paper and concrete materials such as place-value blocks to help students completing the Replay worksheet to model the additions. Encourage the students attempting the Challenge worksheet to explain their working and to check their answers.
Lesson
2
Today we learnt how to add two 3-digit numbers by using place-value blocks. When the total number of ones was 10 or more, we regrouped 10 ones as one ten. When the total number of tens was 10 or more, we regrouped 10 tens as one hundred. How is this concept related to the concept of our base-10?
Replay
Practice
Replay
Topic
Reflection
4
Name
Challenge
Practice
Topic
2
2
Challenge
Topic
Lesson
4
Name
2
Lesson
2
4
Name
Models for Adding 3-Digit Numbers
Models for Adding 3-Digit Numbers
City Squares
Find 152 329.
Write each problem and find the total.
James and Belinda travelled from their hometown, Mathsville, to several different cities. The table shows the distances from Mathsville to each city. Use the distances to divide each city square, shown below, in half. In the squares, each city is represented by the first letter in its name. The total of the distances in one half of the square must equal the total of the distances in the other half.
Step 1: Show each number with place-value blocks.
1
2
243 112 355
37 148 185
Distances from Mathsville to:
3 Cam wants to show 137 1 429 with place-value blocks. She has enough hundreds and ones blocks but only 4 tens blocks. Can she show the problem? Explain. Step 2: Combine the ones.
2 9 11
Step 3: Combine the tens.
50 20 70
Step 4: Combine the hundreds. Step 5: Add.
100 300 400 400 70 11 481
Write each problem and find the total. 1
2
3
4
133 87 220
1
577
7 Harry was playing a board game. He scored 273 points on the first game and 248 points on the second game. How many points did Harry score altogether? A 411
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
B 421
C 511
119 km
Edgarton
249 km
Franksburg
229 km
Grandview
158 km
Highfield
608
2
517
3
478
407 km
A
E
G
A
D
E
B
I
C
H
A
F
588
4 A
or
square kilometres
784
5
359 ADD 570
ADD 211
6
123 SUM 579
SUM 456
7
179 AND 425
AND 246
8
135 ODD 846
ODD 711
metres
D 521
Topic 2 ✪ Addition Concepts and Strategies
178 km
A
F
G
B
G
Replace the letters with numbers that will correctly solve the problem.
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
15
110 km
Denton City
B
321
5 The island of Tonga has an area of 747 square kilometres. The Cook Islands have an area of 263 square kilometres. What is the area of the two islands altogether?
263 248 511
430 km
Centropolis
F
4 Museum A has 127 steps. Museum B has 194 steps. How many steps do the museums have altogether? Place-value blocks may help.
146 134 280
359 km
Bensonville
Irving Glen
No, he does not have enough tens blocks. He needs to have at least 5 tens blocks.
6 The longest cable-stayed bridge in Australia is the ANZAC Bridge at 345 metres. The longest cantilever bridge in Australia is the Storey Bridge. The ANZAC Bridge is 63 metres longer than the Storey Bridge. How many metres long is the Storey Bridge?
256 122 378
Allentown
or the square divided by a horizontal or a vertical rule.
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
Using Models to Add 3-Digit Numbers 15
2
Lesson
3
Adding Whole Numbers Which numbers are in the ones places? [7 and 7.] Why do you need to align place values before adding? [To add correctly.]
Student Activity Book pages
Prevent Misconceptions Why might you begin by estimating the sum? [To check if the exact answer is reasonable.]
2
Adding Whole Numbers
Lesson
3
If an artificial coral reef grew 257 cm last year and 567 cm this year, how much did it grow in total?
Add numbers by adding ones, then tens, then hundreds and then thousands.
Step 1
Grew 567 cm
How do you add whole numbers?
Understand it!
Add 257 567.
Add the ones. Regroup if necessary.
Grew 257 cm
567
Estimate: 300 600 900 Mental Computation Write T for true or F for false next to the following equations. 1 56 89 145 3 135 27 155 5
T
2
F
1 267 321 1 588
T
62 28 92
6
2 689 1 333 4 022
18758
111 24 593 1 6 8 6 1
3567
41454
re
or
U nc
18 eighteen
1 1
257 567 824 The reef grew 824 cm in total.
2 356
9 2 8 3 284
14
5 478
3 7 6 2 9 240
Problem Solving 5a 1 5a Find the following sum. Tip: Look for patterns to help you find shortcuts in computation then describe any patterns you have discovered. 15 18 12 15 18 12 15 18 12 15 18 12 15 18 12 15 18 12 ?
270
11 There were 3 258 fans at the football game in round 1 and 1 761 in round 2. How many fans attended rounds 1 and 2 altogether?
1 3 5
16 153
T
10
13
16 018
ed
5364
T
ct
Independent Practice
12
922 83 1 005
9 2 246 1 3 2 1
Add the hundreds. Regroup if necessary.
Fill in the missing number to make each sum true.
F
4
Guided Practice Find the sum of these numbers. 1 1 7 8 4 543 14 926 8 2 1 3 8 3 2
Step 3
Add the tens. Regroup if necessary. 257 567 24
257 567 4
?? 257
Step 2
1 1
1
Pa g
Visual Learning Bridge (VLB)
If students cannot explain how a column is regrouped, show them that 7 7 14. The four is in the ones place and the one is in the tens place. The extra 10 needs to be regrouped to the tens column where it will be added to the other numbers.
eP
Topic
Explain how you regroup after adding the tens. [5 6 1 12. The 12 tens are regrouped as one hundred and two tens.] Why don’t you need to regroup step three? [The number of hundreds is less than 10, so you don’t need to regroup.]
ro of s
Topic
b b How many different ways can you find the sum? Record the ways then circle your favourite way and explain why you like this way best.
Answers will vary. 5019
nineteen 19 19
Curriculum link: NA073
Problem Solving
15a The sum is 270.
b How many different ways did students come up with? How many students found the pattern 12 15 18 repeats six times and then saw that 12 18 30 so there are six groups of 30 and six groups of 15? (6 3 30) 1 (6 3 15) 5 180 1 90 5 270
16 Topic 2 ✪ Addition Concepts and Strategies
Adding Whole Numbers
16
Or
9 3 30 5 270 6 3 15 is the same as 3 3 30—halve 6 and double 15 keeps the balance—so now you have (6 3 30) 1 (3 3 30) which equals 9 3 30
Or
45 3 6 5 (40 3 6) 1 (5 3 6) 5 240 1 30 5 270 Students may use the multiplication algorithm; however, try to encourage them to use flexible number strategies rather than algorithms to make calculations that they can do in their head.
Year 4 Topic 2 Samples of lesson pages in Teacher Booklet (from Teacher Resource Box 4)
Topic
2
Lesson
3
Topic Focus
Set the Purpose
There is more than one algorithm for each of the operations with rational numbers. Most algorithms for operations with rational numbers, using both mental maths and paper and pencil, use equivalence to transform calculations into simpler ones.
Today you will learn how to add whole numbers involving regrouping.
ro of s
Connect
When might you need to add whole numbers with a sum in the thousands? [Sample answer: Finding the total attendance at a school sports event for a season.] When might you need to add three or more numbers? [Sample answer: Points scored by one player in several games.]
Quick and Easy Lesson Overview Objective Students will add numbers to 100 thousands with and without regrouping.
Explore the Concept
Have students solve the following problems: 288 179; 7 382 425. Allow them to use place-value blocks as needed. Allow time for students to work and then discuss their solutions.
Essential Understanding The standard addition algorithm for multi-digit numbers breaks the calculation into simpler calculations using place value, starting with the ones, then the tens and so on.
eP
Error Intervention
Vocabulary bridging partitioning splitting regrouping
If students are having trouble regrouping digits or forgetting to regroup digits, ask: How can you mark the regrouped digit so it is not forgotten? [Place a box around the regrouped numbers.]
Extension
Maths Background for Teachers
Pa g
Ask students questions such as: What is the smallest number you can add to 527 that would cause regrouping in all three place values? [473] What is the smallest number you can add to 73 that would cause regrouping in both place values? [27]
In this lesson, students should be encouraged to estimate the answer before calculating the problem. Estimation helps students to identify an approximate answer, and allows them to check their calculation against their estimate. If their estimate is completely unlike their answer, one must be wrong.
Small-group Interaction
... while most children are able to solve simple addition problems soon after entering school, a careful building up of addition is required from this first conception to the written and mental forms, using materials to model these problems and generate a language to give meaning to addition statements ... For this reason, a vertical recording of addition is preferable from the outset ...
ed
Work with a small group who may need further instruction, practice or extension. Use blocks, counters and other concrete materials; review the VLA with students; make further connections to real life; or look at one of the Investigations together. Other students work in groups on learning centre activities from the Activity Zone (Minds, Investigations, Games and Digital activity cards, see pages 6–11 of this booklet). Students will record their findings in their Maths Thinking Skills Book.
(Booker et al. 2010)
Reflection In this lesson you learnt how to add numbers up to five digits using regrouping. Why do we need to regroup?
re
ct
Adding whole numbers by writing the calculation builds on the mental calculations and addition of place values from the previous lesson (2.2). Students will benefit from being able to explain how they are performing the mental and written calculation and what is similar about each method.
or
Differentiated Worksheets
U nc
Provide spare paper and concrete materials such as counters to help students completing the Replay worksheet to model the additions. Encourage the students attempting the Challenge worksheet to explain their working and to check their answers.
Replay
Practice
Practice
Topic
2
Lesson
3
4
Name
Adding Whole Numbers Add. 1 1
486 875 45
5
236 223 1 856
1 315
334 948 1 890
2
80 960 4 1 986
6
938 487 1 947
3
2 172
1 406
4
987 096 098 1 945
7
2 030
226 587 1 984
8
2 126
2
3
Step 1 Line up numbers by place value. Add the ones.
World’s Longest Glaciers
456 139 + 547
22 becomes 2 tens and 2 ones.
515 418 362 290
1 2
456 139 + 547
2
1
456 139 + 547
42
945 124 1 343
2
955 017 1 248
5
1 412 4
C 13 052
Continue to regroup.
1 2
1142
3
1 142 is close to the estimate of 1 200.
1 220
588 373 1 866
3
699 311 1 484
6
1 827 1 494
881 735 1 364
1 980
7 Jill added 450 1 790 1 123 and got 1 163. Is this total reasonable?
D 1 152
No, the sum should be closer to 1 400.
13 Leona added 641 1 482 1 879. Should her answer be more than or less than 1 500?
2
24 56 1 15 83
4
5
31 058 20 790 1 18 903 70 751
6
Yes; The answer should be close to 70 000.
300 478 1 213 991
Yes; The answer should be about 1 000.
No; The answer should be close to 100.
566 222 1 532
1 320
224 303 1 125 652
Yes; The answer should be close to 650.
Add.
Length (km)
12 Which is the total of 774 1 276 1 102? B 12 152
Regroup if needed.
Step 3 Add the hundreds, then the thousand.
Regroup if needed.
985 mi
A 1 251
1 Step 2
Add the tens.
Keep digits in neat columns as you add.
Arctic Institute Ice Passage Nimrod-Lennox-King
4
Name
Look at the problem and the answer. Without actually adding the problem, decide whether or not the given answer is reasonable. Write Yes or No and explain your answer.
Estimate: 500 1 100 1 600 5 1 200
2 045
Glacier
3
You can add more than two numbers when you line up the numbers by place value and add one place at a time.
738 234 836 1 237
Lambert-Fisher Ice Passage Novaya Zemlya
Lesson
Use Your Head
No, his answer should be closer to 1 400.
805 mi
2
Adding Whole Numbers
9 Luke added 429 1 699 1 314 and got 950. Is this total reasonable?
11 What is the total combined length of the four longest glaciers in the world?
4
Name
2
10 What is the combined length of the three longest glaciers?
Challenge
Topic
Lesson
Add 456 1 139 1 547.
1 797
2 372
Challenge
Replay
Topic
207 956 1 345 1 217
No; The answer should be about 25 500. 2 341 4 750 1 1 532 80 623
No; The answer should be about 8 600.
Leona’s answer should be more than 1 500.
Topic 2 enVisionMATHS
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 9781442530188
Topic 2 enVisionMATHS
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 9781442530188
Topic 2 enVisionMATHS
Topic 2 ✪ Addition Concepts and Strategies
17
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 9781442530188
Adding Whole Numbers 17
Topic
2
Using Mental Maths to Add
Lesson
1
How can you add with mental maths?
d e t c e r r Unco
Understand it!
Dr Pickford recorded how many whales, dolphins and seals she saw. How many whales did she see during the two weeks?
Numbers can be broken apart to find sums using mental maths.
Find 25 14.
Marine Animals Seen Marine Animals Seen
Animal
Week 1 Week 1
Week 2 Week 2
Whales
25
14
Dolphins
28
17
Seals
34
18
Mental Computation 1 35 26
61
2
50 42
92
Explore 46 the concept 4 71 13 84 61 through watching6 the 5 52 44 96 54 7 Guided Practice Visual Learning Animation Bridge the tens. and viewing the Visual 4 8 8 26 12 26 7 38 26 38 2 24 Learning Bridge on the 30 8 40 24 IWB 38 64 DVD. The Tools4Maths Use partitioning. (11 e-tools) are also on 9 25 12 (20 10 ) (5 2) 10 46 23 (40 20) ( 6 the IWB7 DVD. 60 9 30 3
43 3
37
3)
69
Reasoning 11 How does knowing that 17 2 15 help you to find 28 17 mentally?
Answers will vary. You can bridge the tens by adding 2 to 28 to make 30, and then add the 15 to make 45.
14 fourteen
Curriculum link: NA073
18
Year 4 Topic 2 Sample of Visual Learning Bridge, Animation and Tools4Maths
s f o o r P e g a P d One way
Another way
25 14
25 14
Bridging the tens by adding 5 more to make 30.
Using partitioning by splitting the numbers. Add the tens. Add the ones.
25 14 25 5 9 30 9 39
25 14 (20 10) (5 4) 30 9 39
Dr Pickford saw 39 whales.
Dr Pickford saw 39 whales.
Independent Practice Use partitioning to add mentally. 12 72 18 (70 + 10) + ( 2 + 8)
13 34 25
(30 + 20) + (4 + 5)
80 + 10
50 + 9
90
59
Use bridging the tens to add mentally. 14 47 9 47 + 3 + 6
15 55 37 55 + 5 + 32
50 + 6
60 + 32
56
92
Problem Solving 16a I bought a T-shirt for $26 and a pair of shorts for $27. Use mental maths to find the total cost of the two items.
$53 b How many different ways can you solve this problem? Explain your thinking.
Answers will vary.
For example, you can bridge the tens (26 + 4 + 23 = 30 + 23 = 53) or use partitioning (20 + 20 + 6 + 7 = 40 + 13 = 53). Tools4Maths (available on each enVisionMATHS Interactive Whiteboard DVD)
fifteen 15
19
20
U nc or ed
ct
re ro of s
eP
Pa g
U nc
or
re
ct
ed
Pa g
eP
ro of s
Year 4 Topic 2 Lessons 2.1, 2.2, 2.3 Student Activity Book pages
21
22
U nc or ed
ct
re ro of s
eP
Pa g
U nc
or
re
ct
ed
Pa g
eP
ro of s
Year 4 Topic 2 Lessons 2.1, 2.2, 2.3 Student Activity Book pages
23
24
U nc or ed
ct
re ro of s
eP
Pa g
U nc
or
re
ct
ed
Pa g
eP
ro of s
Year 4 Topic 2 Lessons 2.1, 2.2, 2.3 Student Activity Book pages
25
Topic
2
enVision Minds Addition Concepts and Strategies
CARD A STRATegY
4
Bridging to 100
eP
Pa g
I need to find the total of 178 and 64. I can bridge to the nearest 100 to help add these two numbers in my head. 64 can be broken into 22 + 42 178 + 22 = 200
ed
200 + 42 = 242
How would I work this out in my head?
Add the following numbers using the Bridging to 100 strategy. Take turns to answer each question, and explain your thinking to your partner.
Year 4
1 76 + 37 = ? 2 87 + 29 = ? 3 182 + 46 = ?
4 279 + 48 = ? Make up a question for your partner to answer using the Bridging to 100 strategy. Talk about two situations when you might use the Bridging to 100 strategy in real life. See pages 36 and 37 of this sampler for pages from the Maths Thinking Skills Book where responses to these cards can be recorded.
26
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 3020 1
or
re
ct
So they would need 242 tiles in total.
U nc
Topic 2 Addition Concepts and Strategies CARD A
ro of s
Rudolf and Jane are working out how many tiles they need for their bathroom. They need 178 wall tiles and 64 floor tiles. How many tiles do they need in total?
Samples of Activity Zone Cards: Minds (Mental computation)
enVision Minds
Topic
2
CARD A Quiz
Addition Concepts and Strategies
4
Instructions
ro of s
• Read each question to your partner and ask them to write each answer in their Maths Thinking Skills Book. • Check if their answer is correct and ask them to place a ✓ or a ✗ beside their answer. • Ask them to count the number of ticks and write the number in the ‘Total’ box at the bottom of their page.
4 What is 45 tens plus 3 tens?
ed
5 Add 56 to 35.
Year 4
65 stickers 90 185 48 tens or 480 91 72
7 68 + ? = 76
8
ct
6 What is the total of 23, 27 and 22?
370
9 What is 234 and 100?
334
re
8 What is three hundred and fifty plus twenty?
or
10 What is 54 tens plus 15 tens?
Quiz questions are in groups of 6 with each group being progressively more difficult.
11 Add 124 to 134.
69 tens or 690 258
12 What is the total of 28, 36 and 25?
89
13 86 + ? = 124
38
14 What is four hundred and fifty plus one hundred and thirty?
580
15 What is 432 and 200?
632 71 tens or 710
16 What is 47 tens plus 24 tens? 17 Add 639 to 142.
781
18 What is the total of 47, 33 and 45?
125
27
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 3020 1
eP
3 What is 175 and 10?
Pa g
2 What is seventy plus twenty?
U nc
Topic 2 Addition Concepts and Strategies CARD A
1 Esther had 48 large stickers and 17 small stickers. How many stickers did she have altogether?
Topic
addition Concepts and Strategies
Card a
4
ro of s
2
enVision Investigations
1 Investigate the number of
eP
students in each class at your
Pa g
addition to find the total number
or
2 Explore the width of your foot and other students’ feet. Demonstrate
Year 4
how you could use addition to find out the combined width of your class’s feet. See pages 38 and 39 of this sampler for pages from the Maths Thinking Skills Book where responses to these cards can be recorded.
28
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 3020 1
re
ct
ed
of students in the school.
U nc
Topic 2 addition Concepts and Strategies Card a
school. Show how you could use
Samples of Activity Zone Cards: Investigations
enVision Investigations
Topic
2
4
ro of s
addition Concepts and Strategies
Card a
3 Investigate how many syllables
eP
are in the last name of each
Pa g
you could use addition to find the
re
4 See how far each member of your
or
class can throw a tennis ball and record the results. Demonstrate how you could use addition to find the total distance of all these throws.
29
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 3020 1
Year 4
Investigations are progressively more challenging.
ct
ed
total number of syllables.
U nc
Topic 2 addition Concepts and Strategies Card a
student in your class. Show how
enVision Games
Topic
2
CARD A
4
★
Addition Concepts and Strategies
ro of s
(enVision Games) actual size
• 10 counters in one colour and 10 in another colour • 2 paperclips • 2 dice
You Need or
eP
Take turns. Roll two dice to find your ovals. EXAMPLE: Choose the 3rd oval on the left and the 5th oval on the right, or choose the 5th oval on the left and the 3rd oval on the right. Mark your ovals with paperclips. Explain how to add the numbers by breaking them apart. EXAMPLE: 36 + 19 = (30 + 10) + (6 + 9) and 40 + 15 = 55 Find and cover the answer. Lose your turn if the answer is already taken. The first player or team to get any three connected squares in a row or column wins.
Pa g
on Reflection Icon) actual size
Year 4
U nc Topic 2
45 18
55
ct 73
or
27
re
36
37
61 91
90
54
43
52
46
70
72
99
82
81
36
If you have more time
64
25
64
46 19 54 46
See pages 40 and 41 of this sampler for from the Maths Thinking Skills Play again! Talk about how you break apart the numbers. Play again! Talk about how break apartpages the numbers. Book where responses to these cards can be recorded.
30
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 3020 1
18
ed
Addition Concepts and Strategies CARD A ★
How to Play
Samples of Activity Zone Cards: Games
enVision Games
Topic
2
CARD A
4
★★
Addition Concepts and Strategies
You Need or
• 10 counters in one colour and 10 in another colour • 2 paperclips • 2 dice
Take turns. Roll two dice to find your ovals. EXAMPLE: Choose the 3rd oval on the left and the 5th oval on the right, or choose the 5th oval on the left and the 3rd oval on the right. Mark your ovals with paperclips.
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How to Play
Explain how to add. Make a ten in two different ways. EXAMPLE: 24 + 39 = (24 + 6) + 33 = 30 + 33 = 63 EXAMPLE: 24 + 39 = 23 + (1 + 39) = 23 + 40 = 63 Find and cover the answer. Lose your turn if the answer is already taken. The first player or team to get any three connected squares in a row or column wins.
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There are 1-star and 2-star (more complex) versions of games.
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Play again! Talk about your strategies as you play. again! Talk about your strategies as you play. Play
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Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 3020 1
Addition Concepts and Strategies CARD A ★★
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Addition Concepts and Strategies
(Go Digital Icon) Use: actual size
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1 Go to the Place-value Blocks tool.
2 Click on the Options tab at the bottom of the screen. 3 Click on the down arrow
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twice, click on the Place-value Charts icon
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and choose the Hundreds, Ones Place-value Chart. Click on the OK button.
4 Click on the Maths Mate button at the top of the screen. Your workspace should look like this:
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in the menu at the bottom of the screen and then click 5 Click on the Hundreds icon four times in the HUNDREDS column. Count aloud with each click (“one hundred, two hundred, three hundred etc.”). Check that what you say each time matches the number next to the Maths Mate button at the top of the screen. Stop when you get to 400. Your workspace should now look like this:
Topic 2 Year 4
See page 42 of this sampler for page from the Maths Thinking Skills Book where responses to this card can be recorded.
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Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 3020 1
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Sample of Activity Zone Cards: Digital
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6 Now click on the vertical Tens icon and click twice in the TENS column. Count aloud with each click (“four hundred and ten, four hundred and twenty”). Check that what you say each time matches the number next to the Maths Mate button at the top of the screen. Stop when you get to 420. Your workspace should now look like this:
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and click 7 Now click on the Ones icon three times in the ONES(enVision column. Count aloud Problem Solving) (enVision Language) actual actual click size with each (“four hundred andsize twentyone, four hundred and twenty-two and four hundred and twenty-three”). Check that what you say each time matches the number next to the Maths Mate button at the top of the screen. Stop when you get to 423. Your workspace should now look like this:
(enVision Games) actual size
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five Tens and then two Hundreds. Count aloud with each click and check that what you say each time matches the number next to the Maths Mate button at the top of in the screen. Now click on the Glue icon the toolbar, then click and drag over the 10 ones that need to be regrouped. Click on a highlighted one to regroup your ones. Use the in the toolbar to move the newly Select icon made ten into the TENS column. Your workspace should now look like this:
Follow-up tasks: Use the Hundreds, Tens and Ones icons in the menu at the bottom of the screen to create another number. Count aloud with each click. Challenge your partner to add on another amount where they will need to show regrouping using the Glue icon in the toolbar, to find the total. Can you think of an addition number sentence to show regrouping in the ONES column, and then the TENS column?
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Topic 2 Year 4
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 3020 1
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8 Finally, add on 257 by adding on seven Ones,
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Addition Concepts and Strategies
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Addition Concepts and Strategies
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Introduction The Activity Zone contains games on your topic for you to play with your friends. Your teacher may ask you to record one of the strategies you use to help win these games. You can write these strategies on the red pages in this book. Your teacher may also ask you to add your own ideas to an enVision game you have played; for example, a new theme, easier or harder rules, a different way to win. You can write these ideas on the red pages in this book.
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You will learn mental maths strategies in your maths classes. The yellow enVision Minds cards in the Activity Zone require you to choose a partner, talk about the mental strategy and to ask each other the mental quizzes on the back of the strategy card. Record your results from these cards and questions on the yellow pages in this book.
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In this Maths Thinking Skills Book, you will be able to write and draw your own maths thinking. The pages are divided into different colours, with many of the pages matching the colour of the cards in the Activity Zone.
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Investigations are questions about real-life situations. You will be using many different maths skills to answer these questions. Start by choosing one of the blue Investigations cards on your topic from the Activity Zone, then selecting the question you would like to investigate. Record your working out on the blue pages in this book. The first few blue pages in this book have some questions to guide you, but as you improve your investigation skills you will be able to record your work on the blank blue pages, setting your answers out in your own way.
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enVision Digital When you choose the digital activities from the green cards in the Activity Zone, you can print your work and paste it onto the green pages in this book.
My Reflections At the end of some of your maths lessons, your teacher will ask you to complete a reflection activity on one of the purple pages of this book. At other times, your teacher will talk to you as a class, allowing you to discuss your reflections rather than write them down.
My Maths Language As you learn new maths language, your teacher may ask you to write the new words on the orange pages of this book. You can also include diagrams to help explain the meaning of the words.
Maths Thinking Skills Book 3 to 6 sample pages
enVision Maths w icons for Australia enVision Maths w icons for Australia
enVision Maths new icons for Australia enVision Minds enVision Maths new icons for Australia enVision Minds
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How does the strategy on the card make mental maths easier for you?
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The card asks you to make up a question for your partner. Write the question for your partner here.
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Write the answer to your question here, showing how to use the strategy on the card to get this answer.
Name one of the situations that you discussed where you might use this strategy in real life.
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Maths Thinking Skills Book 3 to 6 sample pages
enVision Minds Quizzes
Answer:
Card:
Date: Topic:
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✓or ✘ Answer:
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Instructions Select a yellow Minds card on your topic from the Activity Zone. • Icon) (enVision Games) (enVision Minds and the card letter (A or B) below. actual number size actual size • Fill in the date, the topic Your partner reads each question. Write your answer below and say it aloud. • • Your partner tells you to place a ✓ or ✘ in the column next to your answer. • Add up the ✓ and write the number in the ‘Total’ box.
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enVision Investigations Structured
Instructions • Write the investigation question, then complete the activity.
Date
Topic no.
Card
Investigation no.
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Investigation question:
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My findings:
How I found a solution:
References I used in this investigation:
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card on your topic from the Activity • Select a blue Investigations (enVision Investigations) (enVision Games) Zone. (enVision Minds Icon) actual size actual size number (1, 2, 3 or 4) below. actual size • Fill in the date, the topic, card A, B or C and the investigation
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Maths Thinking Skills Book 3 to 6 sample pages
enVision Investigations Unstructured
Instructions
Date
Topic no.
Card
Investigation no.
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Investigation question:
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• Write the investigation question, then complete the activity.
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card on your topic from the Activity • Select a blue Investigations (enVision Investigations) (enVision Games) Zone. (enVision Minds Icon) actual size actual size number (1, 2, 3 or 4) below. actual size • Fill in the date, the topic, card A, B or C and the investigation
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enVision Games Strategies
Strategies I Use When Playing enVision Maths Games
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Maths Thinking Skills Book 3 to 6 sample pages
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Some ways I can use the maths I learnt today in my own life: (Include pictures if you like.)
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Year 4 Topic 2 Lessons 2.1, 2.2, 2.3 Differentiated worksheets (from Teacher Resource CD in Teacher Resource Box 4) Topic
2
Replay Lesson
1
4
Name
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Using Mental Maths to Add You can break apart numbers to make them easier to add mentally.
Add 26 1 17 by breaking apart numbers to make a ten.
Break the numbers into tens and ones.
Use a number that adds with the 6 in 26 to make a 10. Since 6 1 4 5 10, use 4.
ones
31 5
30
1
1
45 5
40
1
5
Think: 17 5 4 1 13 Add: 26 1 4 5 30
Add the tens: 30 1 40 5 70 Add the ones: 1 1 5 5 6
Add: 30 1 13 5 43 So, 26 1 17 5 43
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Add the totals: 70 1 6 5 76
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Add 31 1 45 by breaking apart numbers.
So, 31 1 45 5 76
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Find each total using mental maths.
4 25 1 49 5
2 36 1 43 5
3 54 1 23 5
5 37 1 56 5
6 77 1 13 5
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7 To add 32 1 56, Chloe first added 30 1 50. What two steps does she still need to do to find the total? What is Chloe’s total?
8 How can Steve add 48 1 34 by making a ten? What is the total?
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
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Topic
2
Practice Lesson
1
4
Name
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Using Mental Maths to Add Bridge to tens to add mentally. 2 42 1 29 5 42 1
14
5 53 1
3 47 1 41
5 47 1 40 1
19
5 83 1
5 62 1 9
5 87
5 71
So, 53 1 34 5
So, 42 1 29 5
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5
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1 53 1 34
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5 88
So, 47 1 41 5
Use the split strategy to add mentally. 4 27 1 21
5 54 1 12
5 (20 1 20) 1 (7 1
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5 48
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18
5 (50 1 10) 1 (4 1
or
So, 27 1 21 5
)
5 (30 1
) 1 (8 1 1)
5 60 1
5 50 1
5 66
5 59
So, 54 1 12 5
So, 38 1 21 5
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5
)
6 38 1 21
Find each total using mental maths.
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7 52 1 26
11 43 1 38
8 47 1 8
9 32 1 17
10 28 1 31
12 72 1 7
13 42 1 33
14 36 1 14
15 Daniel broke apart a number into 30 1 7. What number did he start with? 16 What is the total of 27 1 42 using mental maths? A 68
B 69
C 78
D 79
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
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Year 4 Topic 2 Lessons 2.1, 2.2, 2.3 Differentiated worksheets (from Teacher Resource CD in Teacher Resource Box 4) Topic
2
Challenge Lesson
1
4
Name
1 Which choice helps the most to solve 43 8? A Think of 8 as 4 4. B Think of 43 as 44 1. C Think of 8 as 10 2.
43 8
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2 Which choice helps the most to solve 67 29? A Think of 67 as 63 4. B Think of 29 as 30 1.
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C Think of 29 as 25 4.
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Explain.
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3 Which choice does not help you solve 63 28 using mental maths? A Think of 63 as 60 3.
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B Think of 28 as 30 2. C Think of 28 as 25 3. Explain.
63 28
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
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Replay
Topic
2
Lesson
2
4
Name
Find 152 329.
Step 2: Combine the ones.
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Step 1: Show each number with place-value blocks.
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Models for Adding 3-Digit Numbers
2 9 11
50 20 70
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Step 3: Combine the tens.
Step 4: Combine the hundreds.
400 70 11 481
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Step 5: Add.
100 300 400
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Write each problem and find the total.
3
4
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
48
Year 4 Topic 2 Lessons 2.1, 2.2, 2.3 Differentiated worksheets (from Teacher Resource CD in Teacher Resource Box 4)
Practice
Topic
2
Lesson
2
4
Name
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Models for Adding 3-Digit Numbers Write each problem and find the total. 2
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3 Cam wants to show 137 1 429 with place-value blocks. She has enough hundreds and ones blocks but only 4 tens blocks. Can she show the problem? Explain.
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4 Museum A has 127 steps. Museum B has 194 steps. How many steps do the museums have altogether? Place-value blocks may help.
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5 The island of Tonga has an area of 747 square kilometres. The Cook Islands have an area of 263 square kilometres. What is the area of the two islands altogether?
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square kilometres
6 The longest cable-stayed bridge in Australia is the ANZAC Bridge at 345 metres. The longest cantilever bridge in Australia is the Storey Bridge. The ANZAC Bridge is 63 metres longer than the Storey Bridge. How many metres long is the Storey Bridge?
metres
7 Harry was playing a board game. He scored 273 points on the first game and 248 points on the second game. How many points did Harry score altogether? A 411
B 421
C 511
D 521
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
49
Challenge
Topic
2
Lesson
2
4
Name
James and Belinda travelled from their hometown, Mathsville, to several different cities. The table shows the distances from Mathsville to each city. Use the distances to divide each city square, shown below, in half. In the squares, each city is represented by the first letter in its name. The total of the distances in one half of the square must equal the total of the distances in the other half.
B
E
I
Distances from Mathsville to: Allentown Bensonville Centropolis
A
C
H
D
A
430 km 110 km 119 km
Edgarton
249 km
Franksburg
229 km
Grandview
158 km
Highfield
407 km
Irving Glen
178 km
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G
359 km
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Denton City
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City Squares
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F
4
A F B G
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Replace the letters with numbers that will correctly solve the problem. 359 ADD 570
6
123 SUM 579
7
179 AND 425
8
135 ODD 846
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5
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
50
Year 4 Topic 2 Lessons 2.1, 2.2, 2.3 Differentiated worksheets (from Teacher Resource CD in Teacher Resource Box 4)
Replay
Topic
2
Lesson
3
4
Name
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Adding Whole Numbers You can add more than two numbers when you line up the numbers by place value and add one place at a time. Add 456 1 139 1 547. Estimate: 500 1 100 1 600 5 1 200
Step 2 Add the tens.
Line up numbers by place value. Regroup if needed. 2
456 139 + 547
22 becomes 2 tens and 2 ones.
12
42
1142
ct
1 142 is close to the estimate of 1 200.
2
588 373 1 866
3
566 222 1 532
5
699 311 1 484
6
881 735 1 364
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945 124 1 343
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Add.
4
12
456 139 + 547
Keep digits in neat columns as you add.
1
Continue to regroup.
456 139 + 547
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2
Add the hundreds, then the thousand.
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Regroup if needed.
Add the ones.
Step 3
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Step 1
955 017 1 248
7 Jill added 450 1 790 1 123 and got 1 163. Is this total reasonable?
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
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Practice
Topic
2
Lesson
3
4
Name
Add.
236 223 1 856
2
334 948 1 890
3
938 487 1 947
6
80 960 4 1 986
7
987 096 098 1 945
4
226 587 1 984
8
738 234 836 1 237
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486 875 1 45
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Adding Whole Numbers
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9 Luke added 429 1 699 1 314 and got 950. Is this total reasonable?
or
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10 What is the combined length of the three longest glaciers?
Glacier
Length (km)
Lambert-Fisher Ice Passage Novaya Zemlya Arctic Institute Ice Passage Nimrod-Lennox-King
515 418 362 290
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11 What is the total combined length of the four longest glaciers in the world?
World’s Longest Glaciers
12 Which is the total of 774 1 276 1 102? A 1 251
B 12 152
C 13 052
D 1 152
13 Leona added 641 1 482 1 879. Should her answer be more than or less than 1 500?
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
52
Year 4 Topic 2 Lessons 2.1, 2.2, 2.3 Differentiated worksheets (from Teacher Resource CD in Teacher Resource Box 4)
Challenge
Topic
2
Lesson
3
4
Name
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Use Your Head Look at the problem and the answer. Without actually adding the problem, decide whether or not the given answer is reasonable. Write Yes or No and explain your answer.
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24 56 1 15 83
300 478 1 213 991
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3
2
4
ed
224 303 1 125 652
207 956 1 345 1 217
6
31 058 20 790 1 18 903 70 751
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5
or
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1
2 341 4 750 1 1 532 80 623
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd), enVisionMATHS Teacher Resource CD 4, 978 1 4425 3018 8
53
Overview of Assessment
Assessment should be more than merely a test at the end of instruction to see how students perform … it should be an integral part of instruction that informs and guides teachers as they make instructional decisions. Assessment should not merely be done to students; rather, it should also be done for students, to guide and enhance their learning. (NCTM 2000, p. 22) The formative assessment tools are used to determine students’ achievements, resulting in action plans, for both teacher and student, in the pursuit of further learning. The summative assessment tools are used to determine an overall measure of achievement at the end of a topic.
Maths Concepts for Addition Concepts and Strategies
3 Addition of Larger Numbers (Lessons 2.3 and 2.4)
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The following assessment tools are available for this enVisionMATHS topic.
Formative Assessment
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Pre-assessment for each maths concept within the topic This pre-assessment helps to gauge the ability of the students in a particular area of mathematics, providing information about a student’s strengths and weaknesses.
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• Prevent misconceptions
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The results of this assessment guide and support teachers in customising instruction for individual student needs. This form of assessment should be administered at the beginning of each topic. It covers both prerequisite material and new content. There are four questions in each pre-assessment: Q1 multiple choice; Q2 short answer; Q3 reasoning; and Q4 problem solving.
• Error intervention
These questions can be more open-ended but not too wordy as they could restrict some students’ access to maths learning due to language barriers.
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2 Models for Adding (Lesson 2.2)
During a Lesson
Short answer (free-response) Free-response assessment helps to eliminate guessing the correct answer. Students answer a question and may have the opportunity to represent their answer pictorially.
Reasoning Students’ reasoning includes their capacity for logical thought and actions such as analysing, proving, evaluating, explaining, inferring, justifying and generalising. The reasoning questions ask students to demonstrate their level of understanding by explaining their thinking behind their choices. This allows teachers to elicit a wealth of information even though the assessment instrument is a written test. Information on students’ reasoning makes it possible to identify misconceptions and inconsistencies. It allows the teacher to identify emerging ideas in students’ thinking so they can be clarified, shared and formalised.
1 Mental Maths (Lesson 2.1)
4 Diagrams for Adding (Lesson 2.5)
Multiple choice Multiple-choice assessment is helpful for teachers to implement a quick and practical assessment task for students. These tests measure students’ levels of mathematical fluency and allow for a quick and direct opportunity for teachers to identify strengths and weaknesses in their students’ maths ability. The multiplechoice style of assessment also reflects that which is used for NAPLAN at Years 3, 5, 7 and 9.
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The focus of assessment in enVisionMATHS is both formative and summative assessment.
Problem solving Problem-solving assessment allows students to demonstrate their problemsolving skills by applying various mathematical problem-solving techniques to non-routine problems. Students are assessed on how they organise information, decode graphic representations, make generalisations and justify conclusions from data. The problem-solving assessment questions appear at the end of each lesson so students have to think about which maths tools or processes they need to apply to formulate their answers. Diagnostic assessments on CD The diagnostic pre- and post-assessments are also found on the Teacher Resource CD for Year 4. While teachers may wish to simply photocopy and administer each assessment as it appears in the following pages, the CD format allows teachers to select and print PDFs of pre- and post-assessments for Year 3, 4 or 5. Further assessment Other opportunities for assessment throughout the program include:
• Small-group interaction
• Differentiated worksheets
or
• observation of a student’s attitude and ability in maths classes
Summative Assessment
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Post-assessment for each maths concept within the topic The post-assessment provides teachers with information about a student’s achievement on a particular topic that has just been studied. These results help the teacher determine whether a student requires revision of or intervention on that topic. It also allows teachers to chart a student’s progress from the beginning of the topic to the end and gives them information to report back to parents. There are four questions in each post-assessment: Q1 multiple choice; Q2 short answer; Q3 reasoning; and Q4 problem solving.
• problem-solving discussion based on each lesson’s problems; for example, identifying and comparing approaches to answers by students • a record of each student’s maths thinking in the various sections of the Maths Thinking Skills Book, including self-assessment through reflection activities.
Observable Skills for Addition Concepts and Strategies • Uses mental maths to calculate addition
Assessment Formats
• Regroups ones to tens, tens to hundreds, hundreds to thousands
Each of these assessments incorporates a range of assessment styles. Different approaches to, and formats for, assessment are required to measure the mathematical knowledge, skills and attitudes of students.
• Adds whole numbers • Adds three or more numbers • Checks calculations with estimating
22 Topic 2
✪ Addition Concepts and Strategies
Overview of Assessment
54
Year 4 Topic 2 Samples of Pre- and Post-assessment pages in Teacher Booklet and Teacher Resource CD (from Teacher Resource Box 4)
Topic
2 Addition Concepts and Strategies
Pre-assessment
Name.......................................................................................... Concept 1: Mental Maths
a.
..55.+.65
b.
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1 Which.of.the.following.add.to.110?.(Use.mental.maths.) ..47.+.63
..55.+.55
..43.+.63
..55.+.45
..47.+.67
..45.+.45
..67.+.53
c.
..100.+.1 ..10.+.1.
..110.+.10 ..100.+.10
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2 Use.mental.maths.to.calculate.the.time.John.is.playing.rugby.when.he.first.goes. on.the.field.for.32.minutes.and.then.goes.on.for.another.12.minutes.
11.=.4.+.7
7.=.11.–.4
__.=.11.–.7
.
Explain.
ed
11.=.7.+.4
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or
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 3011 9
3 What.number.completes.this.number.sentence.family?.
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4 Each.day.for.four.days.Terry.went.jogging..The.first.day.he.jogged.for.35.minutes,. the.second.112.minutes,.the.third.45.minutes,.and.the.fourth.67.minutes..How. many.minutes.did.Terry.jog.over.the.four.days?
Topic 2
23
55
Topic
2 Addition Concepts and Strategies
Pre-assessment
Name.......................................................................................... Concept 2: Models to Add
a.
b.
..
..
c.
..
+ ..
..
..
..
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+
..
..
..
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+
..
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1 Which.of.the.following.models.equals.46?
..
ed
3 Use.the.partitioning.strategy.to.solve.16.+.32..Explain.why.this.strategy.makes.it. easier.
4 What.is.the.missing.number.in.this.number.sentence?.
18.+.29.=.(10.+.8).+.(20.+.___).=.47..Model.using.blocks..
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 3011 9
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2 Write.the.problem.and.find.the.sum.
24 Topic 2
56
Year 4 Topic 2 Samples of Pre- and Post-assessment pages in Teacher Booklet and Teacher Resource CD (from Teacher Resource Box 4)
Topic
2 Addition Concepts and Strategies
Post-assessment
Name.......................................................................................... Concept 1: Mental Maths
a.
..38
b.
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1 Which.is.not.the.same.as.the.others? ..60.+.5
..30.+.8
..70.–.5
..40.–.8
..50.+.15
..40.–.2
..75
c.
..77.+.23
..77.+.3.+.20. ..100
..70.+.10.+.30
eP
2 Use.mental.maths.to.calculate.how.long.in.total.it.took.to.travel.to.the.local.shop.if. you.stopped.after.23.minutes.and.then.still.had.14.minutes.to.go.
Explain.which.strategy.is.easier.for.this.problem.
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3 Use.bridging.the.tens.to.add.mentally:.46.+.8..Then.use.partitioning.to.add. mentally..
re
You.spent.$34.on.a.jacket.and.then.$23.on.a.pair.of.pants..How.much.did.you. spend?
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or
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 3011 9
ct
4 How.many.different.ways.can.you.solve.the.following.problem?.
Topic 2
27
57
Year 4 Topic 2 Samples of Pre- and Post-assessment pages in Teacher Booklet and Teacher Resource CD (from Teacher Resource Box 4)
Topic
2 Addition Concepts and Strategies
Post-assessment
Name.......................................................................................... Concept 2: Models to Add
a.
b.
..
..
c.
+ +
..
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1 Which.of.the.following.models.equals.134? +
+
+ +
..
..
..
..
+
+
..
eP
..
..
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..
..
+
+
+
+
+
+
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3 Does.5.+.3.+.10.=.10.+.5.+.3?.Explain.
4 .On.a.family.trip,.the.Smiths.first.drove.231.km,.then.187.km,.then.25km,. then.122.km..What.is.the.total.distance?.Show.using.a.model.
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 3011 9
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ct
ed
2 Tom.spends.$45,.then.$37,.then.another.$67..How.much.did.he.spend.on.this. shopping.spree.in.total?.Use.a.model.to.show.your.answer.
28 Topic 2
58
Components Chart
A whole new teaching equation teacher resource Box • 12 to 13 topic booklets • Overview and Implementation Guide • Teacher Resource CD with planning documents, worksheets and Visual Learning Bridges
Year
Year
Components Chart
Interactive Whiteboard DVD • Captivating Visual Learning Animations • Visual Learning Bridges • Tools4Maths (11 digital tools) for interactive work
enVisionMATHS is aligned to the Australian Curriculum: Mathematics through direct curriculum links and an instructional design that incorporates the proficiency strands.
AUSTRALIAN
CURRICULUM
student activity Book
activity Zone
maths thinking skills Book
Allows for further conceptual understanding, fluency building, reasoning, mental computation and open-ended problem solving. F–2 books: 96 pages (approx.) 3–6 Books: 232 pages (approx.)
• Laminated topic-based cards, colourcoded and provided in multiples for group work • Investigations, digital activities, games and (for 3–6) mental computation cards • F–2: 2 boxes
• Links directly to the cards activities in the Activity Zone • Allows students to record their maths thinking and reflections • A valuable portfolio of the student’s maths thinking and goals
• 3–6: 1 box
• Both 96 pages
F
978 1 4425 3007 2
978 1 4425 3008 9
978 1 4425 2927 4
978 1 4425 3009 6
978 1 4425 3011 9
978 1 4425 3012 6
978 1 4425 3010 2
978 1 4425 2498 9
1
978 1 4425 3006 5
Year
Year
Year
Year
2
978 1 4425 3014 0
978 1 4425 3015 7
978 1 4425 3013 3
978 1 4425 3016 4
978 1 4425 3023 2
978 1 4425 3024 9
978 1 4425 3022 5
978 1 4425 3025 6
978 1 4425 3018 8
978 1 4425 3019 5
978 1 4425 3017 1
978 1 4425 3020 1
3
4
5 978 1 4425 3021 8
Year
978 1 4425 3027 0
978 1 4425 3028 7
978 1 4425 3026 3
978 1 4425 3029 4
978 1 4425 3031 7
978 1 4425 3032 4
978 1 4425 3030 0
978 1 4425 3033 1
6
www.pearsonplaces.com.au/envision
59
Program Sampler
A whole new teaching equation Victoria & Tasmania
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