Second Grade
Curriculum Unit Plan Second Grade: Mathematics Unit 1: Addition and Subtraction Facts and Place Value Lesson Template Overarching Question: How does understanding place value support addition and subtraction examples in solving word problems? Previous Unit: Place Value, Money, and Fraction Concepts
This Unit: Addition and Subtraction Facts and Place Value
Next Unit: Money and Time
Place Value Concepts
is about
to support
building number sense by understanding place value
reading, writing, and modeling numbers
to support
addition and subtraction strategies
and comparing numbers
to know
to solve
fact families to 20 (doubles & sums to 20)
word problems & equations, e.g., money
Questions to Focus Assessment and Instruction: 1. How does knowledge of place value aid in solving addition problems? 2. How does building fluency in knowing number facts help with basic number combinations for addition and subtraction? 3. How do students model addition and subtraction of whole numbers using different representations? 4. How does using a manipulative such as number cubes help students become more efficient with their number facts? Key Concepts Patterns Commutative property
number models fact family strategies
This document is the property of MAISA.
Intellectual Processes (Standards for Mathematical Practice) • Model understanding of the basic facts using a number line.
composing numbers
equations
June 16, 2011
Second Grade Lesson Abstract In this lesson, students will display their knowledge of properties of objects for sorting and creating patterns. They will also demonstrate an understanding of commutativity and model addition and subtraction of whole numbers using different representations. Students will have an opportunity to practice and become proficient with their addition and subtraction facts. They will identify the facts they still have left to learn and put together a plan for learning them. Common Core Standards Operations and Algebraic Thinking (2.OA) Add and subtract within 20. 2.OA. 2. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Work with equal groups of objects to gain foundations for multiplication. 2.OA.3. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. Number and Operations in Base Ten (2.NBT) Understand place value. 2. NBT.2. Count within 1000; skip-count by 5s, 10s, and 100s. 2. NBT.3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. Instructional Resources Sequence of Lesson Activities Lesson Title: “Let’s Learn Those Facts” http://illuminations.nctm.org/LessonDetail.aspx?ID=L102 One Class Period Materials Needed: crayons number cubes paper counters (16 clear counters per child) “Collect the Counters Activity Sheet” (Control + click to follow link below to access sheet) Enlarge game board to 11X17 http://illuminations.nctm.org/lessons/learnfacts/LearnFacts-AS-CollectTheCounters.pdf Computers for game practice Number line or hundred’s chart (see attached document) Options: two dice/ three dice/ multi-sided dice in place of number cubes Selecting and Setting Up a Mathematical Task: Advance Preparation: What are the mathematical The mathematical objectives of this lesson are to understand the effects of adding objectives for the lesson? and subtracting whole numbers; to develop fluency with basic number combinations for addition and subtraction, and use strategies for whole-number computations, with a focus on addition and subtraction. In what ways does the task build on student’s previous knowledge?
What questions will you ask to access prior knowledge?
Students have been working with sums to 20 since kindergarten. They continue in first grade to learn strategies for addition. The goal is to assist them with practice in this number game toward mastery of common core expectations. They also relate applied properties of operations as strategies to add and subtract (commutative property). • • •
What possible sums can you make when you roll two number cubes? What is the highest sum? The lowest? [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; 12; 2] What rolls of the number cubes will have a sum of 6? Of 10? Of 4? [1+5, 2+4, 3+3; 4+6, 5+5; 1+3, 3:+2.] What was the highest sum you got when you rolled the number cubes? Could you have gotten a higher sum? How do you know? [12; No; 6 and 6 are the largest numbers on the number cubes, and 6 + 6 = 12.]
This document is the property of MAISA.
June 16, 2011
Second Grade
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How can we show that 3 + 6 has the same sum as 6 + 3? What is another way? How can knowing commutativity help you learn the addition facts? [Possible answers include using a calculator, showing by counters, or counting the spots on two number cubes; if you know 6 + 5 = 11, you also know that 5 + 6 = 11.]
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The teacher will place students in groups of up to four students, and provide each group with three number cubes, at least 64 counters and a copy of the “Collect the Counters” activity sheet. Each student will pick a row, write his or her name next to it, and cover each number in that row with a counter. The players will take turns rolling the three number cubes, finding the sums of the numbers, and removing the counter from the sum. It will probably be helpful to play a sample game to allow the teacher to circulate to be sure the students know how to play.
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Launch: • How would you introduce the activity to the students?
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In this game, there are 16 possible sums that can result when three number cubes are tossed, namely 3-18. (Obviously, some of these sums are most likely than others. As students roll and attain various sums, they remove the counters from the game board. For instance, if a student had rolled four times and obtained sums of 7, 11, 13, and 17, their game board would look like this:
Highlighted numbers would be uncovered.
What will be heard that indicates the students understood what the task is asking them to do?
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 •
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• Explore What questions will be asked to focus student’s thinking on the key ideas?
How will you extend the task to provide additional challenge?
You can adjust the rules for winning depending on how much time you would like students to spend playing this game. In the longest version, play until one student has removed all of the counters. (Note that the probability of rolling a 3 or an 18 is only 1/216, so it may take a while for these rolls to appear.) In shorter versions, play until a student removes 3, 4, or 5 counters in a row. (Asking students to identify the counters in a row that were removed by the winner can lead to a good discussion about probability and why some sums are more likely than others.) Asking students to identify the counters in a row that were removed by the winner can lead to a good discussion about probability and why some sums are more likely than others.
The next step is to introduce the students to the Math Fact Practice website which provides an opportunity for students to practice their facts and develop fluency in recalling them. (control+ click to follow link below) http://www.playkidsgames.com/games/mathfact/mathFact.htm 1. Select math fact practice type. 2. Select difficulty and maximum number for the operands or select dynamic for automatic adjustment of difficulty level. 3. Select math operations and duration of practice, then start. 4. Continue to answer problems using keypad. 5. Use skip to reveal the answer. 6. The end of the game will show a report of average time spent per problem by math operation and level. • Students may select from among the four binary operations, addition, subtraction, multiplication, division and the level of difficulty. This will give
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June 16, 2011
Second Grade What questions will be asked to assess understanding of key mathematical ideas?
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the teacher an opportunity to provide for differentiation opportunities for all students. Proficiency can be monitored by using the Summary Sheet at the end of the practice session. This printable document gives the teacher information about the number of problems answered, the time it took to answer, the operation(s) used, and the number skipped. Students can be asked to model on the number line some of the equations. (See number line attached.) They can also model on the hundred’s chart. For example, show me some ways to get to the sum of 12 on the number line. Students can model 6+ 6, 10+ 2, 7+ 5, 8+ 4, 11+1, etc. They could also show how to subtract numbers to get to 12 such as 15-3, 20-6, etc. or even model multiplication facts such as 3X4, 6X2, or 3X3X2…
Summary •
What specific questions will be asked so that students make connections between the different strategies that are presented?
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What will be seen or heard that indicates all students understand the mathematical ideas you intended them to learn?
This lesson gives students a chance to revisit and become proficient with their basic facts in an engaging way. Prior to this the students will have been working on strategies to learn their facts so that they can access them in a timely, efficient way. The teacher can ask the following questions and students can jot down their answers on their slates or a piece of paper (Paper/pencil assessment attached): 1. What is the sum of 4 + 3? (7) 2. What other number pairs have the same sum? ( 0+7, 1+6, 2+5) 3. What pairs of numbers has a sum of nine? (0+9, 1+8, 2+7,3+6,4+5) Are there any others with that sum? 4. What do you know about 3+7 if you know the sum of 7+ 3? (The sum for both is 10) 5. What property is this? ( the commutative property) 6. What number combinations are there to three? (0+3, 1+2) 7. What number combinations are there to eleven? (0+11, 1+10, 2+9, 3+8, 4+7, 5+6) 8. What number combinations are there to five? (0+5, 1+4, 2+3) These are all good practices that can be supported orally or in written format. Engaging students in opportunities to practice their facts in distributed practice helps them become proficient and have those facts easily accessible as they work with multi-step problems. Can the students explain how to find products on an addition chart?
Teacher Reflection: This is an important part of the lesson that informs instruction. The teacher should take time to think about the following questions in response to student learning: • Which students need more time to practice the addition facts? How will I provide this practice? Programs like Everyday Math provide more games like “Name that Number” or versions of card games that provide opportunities for individual student practice. • What other experiences will be helpful to the students who still have several facts to learn? • Which activities will foster individual remediation? • How will I assure that the whole class has an opportunity for frequent practice with addition and subtraction facts? • What topics will require mastery of the addition facts? • What adjustment will I make the next time that I teach this lesson? • Are there appropriate extension activities for students who have mastered their facts?
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June 16, 2011
Second Grade • • • • • • •
Do the students recognize the facts they know and those they have yet to learn? How can I help provide continued practice of the addition facts for students who are proficient with them? What other learning experiences will help students explore addition as a natural part of daily activity? How might I connect the fundamental ideas of this unit with lessons about related mathematics content? What learning experiences would help the students not yet comfortable with these concepts to continue toward mastery of the addition facts? What experiences would help the students extend their current level of understanding of this topic? How will I provide brief, focused fact reviews throughout the year?
Board Games: Games are a very motivating opportunity for students to work on their facts. Games such as: Monkey Math Game 1-2-3 Oy! FISHIN’ FOR ADDITION THE ADDITION FACTS CARD GAME ZAP Addition Math Card Game
This document is the property of MAISA.
June 16, 2011
