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Grade 1: Measurement - How Long Is It? Addition and Subtraction in Other Strands Texas Essential Knowledge and Skills (TEKS): (1.1) Number, operation, and quantitative reasoning. The student uses whole numbers to describe and compare quantities. The student is expected to: (A) Compare and order whole numbers up to 99 (less than, greater than, or equal to) using sets of concrete objects and pictorial models; (B) Create sets of tens and ones using concrete objects to describe, compare, and order whole numbers; and (D) Read and write numbers to 99 to describe sets of concrete objects. (1.3) Number, operation, and quantitative reasoning. The student recognizes and solves problems in addition and subtraction situations. The student is expected to: (A) Model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences; and (B) Use concrete and pictorial models to apply basic addition and subtraction facts (up to 9 + 9 = 18 and 18 – 9 = 9).
TEKS Connections to other Strands: (1.7) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and temperature. The student uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length. The student is expected to: (A) Estimate and measure length using nonstandard units such as paper clips or sides of color tiles; (B) Compare and order two or more concrete objects according to length (from longest to shortest); and (C) Describe the relationship between the size of the unit and the number of units needed to measure the length of an object; (1.11) Underlying processes and mathematical tools. The student applies Grade 1 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: (A) Identify mathematics in everyday situations; and (D) Use tools such as real objects, manipulatives, and technology to solve problems. (1.12) Underlying processes and mathematical tools. The student communicates about Grade 1 mathematics using informal language. The student is expected to: (A) Explain and record observations using objects, words, pictures, numbers, and technology; and (B) Relate informal language to mathematical language and symbols. (1.13) Underlying processes and mathematical tools. The student uses logical reasoning. The student is expected to: Justify his or her thinking using objects, words, pictures, numbers, and technology.
Mathematics TEKS Connections: Grades K-2 Session 3: Addition and Subtraction – Grade 1
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Purpose: The focus of this lesson is linear measurement with non-standard units. The direct measurement of concrete objects provides the opportunity for students to develop counting strategies as well as addition and subtraction concepts as students find the length of an object and compare the length of sides.
Grouping: Whole class, small groups, pairs Suggested Vocabulary: add compare join
length measure order
separate subtract units
Materials: (Tools for measuring are limited to classroom resources. You are not limited to the suggested manipulatives below.) • 1-inch cubes • 1-inch square colored tiles such as Color Tiles • Paper clips • Linking cubes • Unsharpened pencils • Student hands • Strips of paper cut to the same length • Object signs with spelled word and picture of an object • Handout 1-1: Measuring Tool Signs - run on cardstock, cut apart, one card per station Advanced Preparation: • Set up measuring stations through which the students will rotate. There should be at least one measuring station for every four students. For Each Student: • Handout 1-2: Measurement Recording Sheet • Handout 1-3: Classroom Station Measurements • Handout 1-4: How Long Is It? • Handout 1-5: Ten-Frames • Handout 1-6: Cube Organizer (optional) • Chart paper
Suggested Pacing: •
3-5 days
Mathematics TEKS Connections: Grades K-2 Session 3: Addition and Subtraction – Grade 1
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Procedures: Engage: 1. Set up the context for measuring by telling the students you are thinking about making some changes in the classroom. Tell students that you need their help to measure several things in the classroom so you will know if items will fit where you want to put them. • Have you ever measured anything before? Responses may vary. • What would be good tools to use for measuring? Responses may vary. • What tools have you used at home for measuring? Responses may vary. 2. If measuring is new to the students, the teacher may need to demonstrate. If the students have been exposed to measuring, remind students how to measure by having two or three students demonstrate for the class how they would measure the top of a student desk with one of the mentioned tools. Guide students through measuring by asking the following questions. • How many sides does the top of the desk have? Responses may vary.
Teacher Notes: Allow students to share measurement experiences and ideas about different tools they can use. Accept all answers. Tools are limited to classroom resources. • •
Observe students as they demonstrate measuring their desks. Check to see that students are placing the non-standard units appropriately and consistently to measure.
Example Paper clips are placed end to end in one direction.
Measure one side of the desk. • How long is the desk? Responses may vary. If students are struggling, use the following example: Demonstrate how to measure with paper clips. Place both large clips and small paper clips on the table. • •
What do you notice about the paper clips? Responses may vary. Possible responses include: They are not the same length. Can both of these clips be used at the same time when measuring the length of this table? No, we have to define the tool. Either use the large paper clips or the small paper clips.
Mathematics TEKS Connections: Grades K-2 Session 3: Addition and Subtraction – Grade 1
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Grade 1 Begin by placing a large paper clip along an edge of the table. Place the next paper clip in the same direction as the first (probably with the length the longest); the second paper clip should be touching the first – not overlapping - and with no gaps. As other paper clips are added onto the chain, the paperclips should be as straight as possible. • About how many large paper clips do you think it will take to measure the length? Responses may vary.
Note: Paper Clip Demonstration Using a connected chain of paper clips may be easier if students are struggling with the alignment. Just make sure the chain is pulled tight. Another option is to change to larger tool such as popsicle sticks, which is easier for little fingers to manipulate.
After the students predict, have a volunteer measure and report the length. Make sure the student labels the answer as large paper clips. • Did all of the paper clips fit perfectly when we were measuring the length of the table? Responses may vary. Be aware that the measurement tool may not fit perfectly the length of item being measured. Discuss this possibility with the students. Will the students count only the measuring objects that fit on the table without hanging over the side, or will they count the measuring objects that come closest to the length of the item being measured (sticks over just a little bit)? Make sure all students agree upon the decision made by the class. Have students predict the length of another side of the table. • Do you think it will be longer or shorter? Will it take more clips or less clips? Are the measurements for the sides the same? Responses may vary. Let’s measure and find out. Explain your answer.
Mathematics TEKS Connections: Grades K-2 Session 3: Addition and Subtraction – Grade 1
It is very important to build estimation skills by always having the students estimate first. This is an excellent time to asses informally how the students count. Did they count as they laid each clip down or did they count at the end? Did they point and count aloud by ones or skip-count? Ex: 1 paper clip, two paper clips, etc. or 26 large paper clips. STRESS THE LABEL.
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Grade 1 3. Guide students through a wrap-up discussion about how to properly measure. • How many different tools did we use to measure the length? Responses may vary. • What measuring tool was used? How do you place the paper clips to measure? Why? Responses may vary. • Always do what before measuring? Estimate • How do we label our answer? With the tool that is being used 4. Handout 1-2: Measurement Recording Sheet. Model how students should record the name of their measuring tool, the object being measured, and its measurements.
Handout 1-2: Measurement Recording Sheet
5. Tell the students they will be working in pairs to measure different objects in the classroom. Two pairs can work in one station at a time. Set up of stations: Label all sides you want students to measure as Advance Preparation required in Explore Phase: Set up Side 1, Side 2, Side 3, and Side 4. measuring stations through which the students will rotate. There should be at least one measuring station for Choose measuring tools and objects to be measured that keep the every four students. numbers relatively small (20 or less). Examples: book and colored tiles, bookcase and sentence strips. All objects should be rectangular shapes and may be squares.
Explore:
1. Provide each pair of students with a Handout 1-2: Measurement Recording Sheet (recorded information will be used in the Explain phase). Point out the different measurement stations around the room.
Handout 1-2: Measurement Recording Sheet
Show students that each station has a different measurement tool ready for them to use.
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Grade 1 Instruct students to use the tools represented on the signs at the station to measure the object at each station. Refer to Handout 1-2: Measurement Recording Sheet and Handout 1-1: Measuring Tool Signs as a reminder of the measuring tools and their names.
Handout 1-1: Measuring Tool Signs
Remind students of the Measurement Recording Sheet and how to record the name of the measuring tool, the object being measured, and its measurements. Each student needs to measure and verify the measurement with his or her partner.
Having a picture along with the name helps English language learners to know the tool being referenced.
Demonstrate how you want students to move from station to station. 2. Monitor students as they measure in the various stations. Support students with questions to gain insight into their strategies as they count the units when they measure. • How many units long is this side? Responses may vary. • Can you show me how you measured this? Responses may vary. • What is another way to count your units? Responses may vary. • Did your partner get the same measurement? Responses may vary.
Mathematics TEKS Connections: Grades K-2 Session 3: Addition and Subtraction – Grade 1
Keep track of different strategies the children use as they measure. • Are students counting one unit at a time? • Are they using grouping strategies (by 2s, 5s,10s)? You will want to make sure the strategies are shared during the Explain phase. Research First graders do not understand the concept of length as an attribute of an object. However, they can count the number of units. Counting and comparing numbers will help students begin to develop the relationship of the size of a unit and the number of units needed to measure (Van de Walle, J.A., 2004).
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Explain: 1. Bring the class back together to compare measurements. Students need their recording sheets. 2. Use an overhead copy of Handout 1-3: Classroom Station Measurements to record students’ measurements.
3. Call on different pairs of students to complete the chart.
Handout 1-3: Classroom Station Measurements
The chart will be used to set up addition and subtraction problems in the Elaborate phase. There will be different length measurements for stations that have two different size tools (the station where students are measuring with their hands).
Ask students to demonstrate how they measured.
Guide students to understand that how they place the measurement tool matters for consistency in measuring. Example: A popsicle stick placed vertically versus a popsicle stick placed horizontally.
Discuss different measurements for the same sides using the same tools. • Why do you think the measurements are different? Responses may vary. • How does the size of the measuring tool affect the number of units when measuring? Responses may vary.
Call on two students with obviously different size hands to demonstrate why the measurements are different. TEKS Connection: 1.7C: First grade lays the foundation for developing the understanding of the relationship between the size of the unit and the number of units needed. Students will need numerous measurement experiences throughout the year to develop and reinforce this relational understanding.
Elaborate: 1.
Work with small groups to extend the lesson with addition and subtraction.
2. Use Handout 1-3: Classroom Station Measurements created in the Explore Phase to model addition and subtraction situations. Mathematics TEKS Connections: Grades K-2 Session 3: Addition and Subtraction – Grade 1
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Grade 1 3. Refer to a specific object that was measured. Tell students they will be adding and subtracting and may select from any of the available tools. Give each group a copy of Handout 1-5: Ten-Frames. Provide students with counters, paper clips, or other manipulatives such as linking cubes. To help students visualize the number and determine the value of the number, provide groups with a plastic Ten-Frame or a Ten-Frame mat. Teacher refers to Handout 1-3: Classroom Station Measurement orally to present the following problems. Students are not recording during this questioning. Teachers are observing student performance. Scenario 1: Joining (Adding) two numbers. Object A (say the name of the specific object) measures _____units on side 1, _____units on side 2, _____units on side 3, _____units on side 4. • For object A, are there any equal sides? Responses may vary. • How can you describe where these sides are on Object A? Responses may vary. • Compare two non-equal sides on Object A, which side is longer? Which side is shorter? Responses may vary. • How much longer is side # than side #? Responses may vary. Tell students you want to combine the lengths of all the sides. Have students build the number of units on side 1 in the first Ten-Frame and the number of units in side 2 in the second Ten-Frame. To Join side 1 and side 2 lengths, we need to join the TenFrames. Move objects from one Ten-Frame to the other Ten-Frame until the second Ten-Frame is completely full. Next, model the length of side 3 in a Ten-Frame and join side 3 with the Ten-Frame containing side 1 and side 2’s objects. Continue this process with side 4. You now have combined all the side lengths and all objects are in a Ten-Frame. The total number of objects tells the length of the outside of Object A or its perimeter.
Mathematics TEKS Connections: Grades K-2 Session 3: Addition and Subtraction – Grade 1
Handout 1-5: Ten-Frames
Handout 1-6: Cube organizer can be used to help students with scenarios 1 and 2 (adding and separating). Observe the strategies students use to model addition and subtraction. • Do students count out each number and then count each counter one by one? • Do students regroup the counters to count by 2s, 5s, or 10s? • Do students model the first number, then the second number and count on from the first number? • Do students model both numbers, then count on from the larger number? • How do students compare numbers? • Do they line the numbers side by side and count the non-paired counters? • Do students model the larger number and take away the smaller number? 4 1 3 2
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Grade 1 Scenario 2: Separating (Subtracting) two numbers Object B has a total of _____units in all. Sides 1 and 3 are _____units together. How many units long are sides 2 and 4 together? Instruct the students to build the total number of units in the Ten-Frames. Then provide the students with additional Ten-Frames. Have the students separate the number of units from the total TenFrame to the Ten-Frame representing sides 1 and 3. •
If we separate the units of sides 1 and 3 from the total number of units, what will the remaining objects represent? The remaining units in the total Ten-Frame will end up representing the length of sides 2 and 4.
Teacher Note This is a great opportunity to demonstrate a part/part/whole relationship: the two equal sides 1 and 3 and the other two equal sides 2 and 4 together equal the total units. It is also a great opportunity for students to see that addition and subtraction are inverse relationships and the equal sides bring in repeated addition and subtraction. 4 1 3 2
Should students not understand that when sides 1 and 3 objects are separated from the total TenFrame, the remaining units are sides 2 and 4, have them build sides 1 and 3 and then compare sides 2 and 4 to the remaining total Ten-Frame.
Note: Students need multiple opportunities to explore the process of joining and separating before attempting Handout 1-4: How Long Is It? After students have many experiences with the TenFrames, the teacher should introduce Handout 1-4: How Long Is It?. It is recommended that the teacher model how to complete the recording sheet when asking students to complete Handout 1-4: How Long Is It?.
Mathematics TEKS Connections: Grades K-2 Session 3: Addition and Subtraction – Grade 1
Students may also notice the total length of sides 1 and 2 is equal to the length of sides 3 and 4. This observation will eventually lead to building the perimeter formula in upper grades: p= 2(l +w) or p= 2l +2w. This is NOT part of this lesson or part of the Grade 1 TEKS, but for teacher background knowledge only.
Handout 1- 4: How Long Is It?
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Grade 1 4. Have students share the various strategies used to solve the problems. Have organizers available for students such as Handout 1-5: Ten-Frames, the Handout 1-6: Cube Organizer, or other organizers to help model the problems.
Research “Over time, these physical modeling strategies give way to more efficient counting strategies which are generally more abstract ways of modeling a problem. Eventually, children come to rely on number facts, but the learning of number facts is not necessarily rote skill. It can build upon an understanding of number relations, which are supported by a foundation of number sense developed through using modeling and counting strategies” (Carpenter, et al, 1999, p. 4).
Prior to Evaluate 1. In small groups provide Handout 1-4: How Long Is • Label the two objects you want students to measure with Side 1, It?, measuring tools, Ten-Frames and two objects Side 2, Side 3, and Side 4. for students to measure. • Choose measuring tools and 2. Instruct the students to select a measuring tool and objects to be measured that keep measure the two objects. Students need to complete the numbers relatively small (20 How Long Is It? or less). Extensions: • Create a class book for the measures of classroom objects. Have each child illustrate and measure a different class object. The completed book can go in the classroom library. • Create a center for measuring objects that includes adding/joining and subtracting/separating tasks.
Evaluate:
Mathematics TEKS Connections: Grades K-2 Session 3: Addition and Subtraction – Grade 1
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Handout 1-1: Measuring Tool Signs Color Tiles
1-inch Cubes
Pencils (unsharpened)
Student Hand
Paper Clips
Linking Cubes
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Handout 1-2: Measurement Recording Sheet Station 1
Station 2
Measuring Tool: _____________________
Measuring Tool: _____________________
__________________________________ Classroom Object
__________________________________ Classroom Object
Side 1_______units
Side 2_______units
Side 1_______units
Side 2_______units
Side 3_______units
Side 4_______units
Side 3_______units
Side 4_______units
Station 3
Station 4
Measuring Tool: _____________________
Measuring Tool: _____________________
__________________________________ Classroom Object
__________________________________ Classroom Object
Side 1_______units
Side 2_______units
Side 1_______units
Side 2_______units
Side 3_______units
Side 4_______units
Side 3_______units
Side 4_______units
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Handout 1-2: Measurement Recording Sheet (page 2) Station 5
Station 6
Measuring Tool: _____________________
Measuring Tool: _____________________
__________________________________ Classroom Object
__________________________________ Classroom Object
Side 1_______units
Side 2_______units
Side 1_______units
Side 2_______units
Side 3_______units
Side 4_______units
Side 3_______units
Side 4_______units
Station 7
Station 8
Measuring Tool: _____________________
Measuring Tool: _____________________
__________________________________ Classroom Object
__________________________________ Classroom Object
Side 1_______units
Side 2_______units
Side 1_______units
Side 2_______units
Side 3_______units
Side 4_______units
Side 3_______units
Side 4_______units
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Handout 1-3: Classroom Station Measurements Name: ________________________________
Station Number
Object
Side 1
Date: _______________________
Side 2
Side 3
Side 4
1
2
3
4
5
6
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Handout 1-4: How Long Is It? Object 1 Measuring Tool _________________ Name of Object _______________________________
Side 1__________ Side 2__________ Side 3__________ Side 4__________ How many units for all sides (perimeter)? ________ Number sentence: ___________________________ -------------------------------------------------------------------------------------------------------------------------
Object 2
Measuring Tool _________________ Name of Object _______________________________
Side 1__________ Side 2__________ Side 3__________ Side 4__________
Are any sides equal? __________ If yes, which sides are equal? ____________ Which side is the longest? _________________ How much longer is the longest side? ______________ Number sentence: _________________________________________ Mathematics TEKS Connections: Grades K-2 Session 3: Addition and Subtraction – Grade 1
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Handout 1-5: Ten-Frames
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Handout 1-6: Cube Organizer
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