# Exploring Length, Area, and Attributes

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1 Explorations Exploring Length, Area, and Attributes Objectives To guide children as they measure lengths and distances to the nearest inch and centimeter, explore area by tiling surfaces, and sort attribute blocks according to rules. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Key Concepts and Skills Distinguish between centimeter and inch. [Measurement and Reference Frames Goal 1] Compare lengths in centimeters and. [Measurement and Reference Frames Goal 1] Measure to the nearest in. and cm. [Measurement and Reference Frames Goal 1] Find area by tiling with pattern blocks and counting shapes. [Measurement and Reference Frames Goal ] Use rules to sort attribute blocks. [Patterns, Functions, and Algebra Goal 1] Playing Beat the Calculator Math Journal 1, p. 4 My Reference Book, pp. 14 and 15 1 calculator per child Math Boxes Math Journal 1, p. 104 Home Link Math Masters, p. 110 Key Activities Children examine and discuss inch and centimeter scales. Exploration D: Children use a tape measure to measure lengths and distances. Exploration E: Children use concrete materials to tile surfaces. Exploration F: Children sort attribute blocks according to rules. Key Vocabulary inch (in.) centimeter (cm) tiling attribute blocks Materials Home Link 4 6 tape measure and yardstick Exploration D: Per group: Math Journal 1, pp. 99 and 100 tape measure Exploration E: Per partnership: Math Journal 1, pp. 101 and 10 pattern blocks Pattern-Block Template playing cards or Everything Math Deck, if available slate sheets of paper scissors Exploration F: Per group: Math Journal 1, p. 103 Math Masters, pp set of attribute blocks scissors envelope sheets of paper red, yellow, and blue crayons Differentiation Options ENRICHMENT Finding More Than One Way Math Journal 1, pp. 99 and 100 tape measure ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. 14 Advance Preparation Children should write tool-kit numbers on their tape measures. For a mathematics and literacy connection, obtain copies of A Cloak for the Dreamer by Aileen Friedman (Scholastic Inc., 1995) and Inch by Inch by Leo Lionni (HarperCollins Publishers, 1995). Teacher s Reference Manual, Grades 1 3 pp , 14 8 Unit 4 Addition and Subtraction

2 Getting Started Mental Math and Reflexes Pose problems like these: 95-5 =? =? 70? = ? = =? =? Math Message Name two things you would measure with a ruler. Name two things you would measure with a tape measure. Home Link 4 6 Follow-Up Ask volunteers to explain how they solved each problem. Assess whether most children were able to find the answers to the problems mentally. 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS DISCUSSION Discuss children s answers. Sample answers: ruler: the width of a hand, the length of a crayon; tape measure: the width of a desk, the distance around a person s waist It is important to select the correct measuring tool for the task at hand. Children s tool-kit rulers are best suited for measuring lengths and distances that are shorter than the ruler. Tape measures and yardsticks are longer. They are used to measure longer lengths. Tape measures are also useful for measuring things that are not flat, and for measuring around things. Pull out a tool-kit tape measure to its full length (5 feet) and hold this alongside a yardstick. Ask why the tape measure would be a more convenient tool than the yardstick for measuring the heights of children in the class. Sample answer: Most of the children are taller than a yardstick, but shorter than the 5-foot tape. NOTE To demonstrate the inverse relationship between the size of a unit and the number of units used, use an inch ruler and a centimeter ruler to measure the width of a book. Help children see that it takes fewer units to measure something with a large unit () than with a small one (centimeters). Examining Inch and Centimeter Scales WHOLE-CLASS DISCUSSION Discuss the inch (in.) and centimeter (cm) scales on rulers and tape measures. Ask children to examine their rulers and tape measures, and ensure that they can correctly identify the two scales on each. Explain the inch scale is more commonly used in the United States. In science, lengths are reported in centimeters or other metric units. Write the units and their abbreviations on the board. Ask children which unit is longer the inch or the centimeter. The inch Have children carefully pull their tape measures out to their full lengths. How long is your tape measure? 60 on the inch side; 150 cm on the centimeter side NOTE If children are using retractable tape measures, teach and enforce the -inch, no zap rule: You may zap the tape measure only when no more than are showing. Following this rule will extend the life of the tape measures. Lesson 83

3 Measuring Lengths with a Tape Measure cont. 4. Open your journal so it looks like the drawing below. a. Measure the long side and the short side to the nearest inch. The long side is 17. The short side is 11. b. Now measure your journal to the nearest centimeter. The long side is 44 centimeters. The short side is 8 centimeters. short side Measuring Lengths with a Tape Measure 1. Measure the height from the top of your desk or table to the floor. Measure to the nearest inch and centimeter. The height from my desk or table to the floor is. Answers vary. The height from my desk or table to the floor is centimeters.. Measure the height from the top of your chair to the floor. Measure to the nearest inch and centimeter. The height from the top of my chair to the floor is. Answers vary. The height from the top of my chair to the floor is centimeters. 3. Measure the width of your classroom door. The classroom door is wide. Answers vary. The classroom door is centimeters wide. Math Journal 1, p. 99 EM3cuGMJ1_U04_80_111.indd 99 Adjusting the Activity Have children find an object in your classroom that is 50 long. Then have them find an object in your classroom that is 50 centimeters long. AUDITORY KINESTHETIC TACTILE VISUAL long side Journal 1/1/11 :7 PM Ask children to compare lengths on the two sides of their tape measures at different points along the tape. For example: It s 0 on the inch side and 51 on the centimeter side. It s 30 on the inch side and 76 on the centimeter side. It s 100 on the centimeter side and 39 on the inch side. Help children summarize the comparison. If you measure a length in centimeters, you will get a larger number than if you measure the same length in. Exploration D: Measuring Lengths with a Tape Measure (Math Journal 1, pp. 99 and 100) SMALL-GROUP Children who used Everyday Mathematics in first grade have had considerable practice using rulers and tape measures to measure lengths to the nearest inch, but limited practice in measuring to the nearest centimeter. As you circulate, make sure children are lining up one end of the object or distance to be measured with the end (zero mark) of the tape measure. If a measured length falls between the inch (or centimeter) marks on their tapes, some children may need help deciding which is the nearest inch (or centimeter). Exploration E: Tiling Surfaces with Informal Units (Math Journal 1, pp. 101 and 10) PARTNER ELL Children use multiples of square pattern blocks to cover a playing card as completely as possible. There should be no spaces between the blocks, nor should the blocks overlap or extend beyond the card. This activity is called tiling. To support English language learners, discuss the meaning of the words tile and tiling. Ask the children if they have tiles in their homes or if they see any in the classroom. Children record the number of pattern-block squares needed to tile the card. Any space around the edges of the card that cannot be covered by a whole block but that can be covered by more than half a block can be counted as 1 block. Any uncovered spaces less than half of a block should not be counted. Next, children tile their slates and templates with playing cards and record the result. Then they fold an 8 1_ " by 11" sheet of paper into fourths, cut out the fourths, and use them to tile larger items, such as their desktops or a tabletop. Again, they record what they did. Ask children to find things in the room that are tiled or covered with a pattern. Math Journal 1, p. 100 EM3cuGMJ1_U04_80_111.indd 100 1//10 1:01 PM 84 Unit 4 Addition and Subtraction

4 Exploration F: Sorting Attribute Blocks (Math Journal 1, p. 103; Math Masters, pp ) Algebraic Thinking Children sort attribute blocks with these steps: 1. Cut apart the cards on Math Masters, page 109. PROBLEM SOLVING. Shuffle the cards and put them in a pile facedown. SMALL-GROUP 3. Label one sheet of paper These Fit the Rule. Label a second sheet These Do Not Fit the Rule. 4. Children take turns being the Rule Maker. The Rule Maker draws a card from the shuffled pile and puts it out for all to see. 5. The other children take turns putting blocks on the appropriate sheets labeled These Fit the Rule and These Do Not Fit the Rule. Children record one of their rules on journal page 103 and describe those attribute blocks that fit the rule and those that don t. Materials Tiling Surfaces with Shapes square pattern blocks slates sheets of paper Pattern-Block Template scissors Everything Math Deck cards, if available 1. Use square pattern blocks. Tile a card by covering it with the square pattern blocks. Lay the blocks flat on the card. Don t leave any spaces between blocks. Keep the blocks inside the edges of the card. There may be open spaces along the edges. Count the blocks on the card. If a space could be covered by more than half of a block, count the space as one block. Do not count spaces that could be covered by less than half of a block. Number of square pattern blocks needed to tile the card: EM3cuGMJ1_U04_80_111.indd 101 Answers vary. Trace the card. Use your Pattern-Block Template to draw the square pattern blocks you used to tile the card. Math Journal 1, p /0/10 5:16 PM Adjusting the Activity Encourage children to work in partnerships when taking turns putting blocks on the appropriate sheet. In this way, children are able to discuss their choices. Alternately, the whole group can work together as a team to decide which blocks fit the rule and which do not. Have children make up their own rules and write them on the two blank cards on Math Masters, page 109. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L NOTE The Attribute Rule Cards from Math Masters, page 109 will be needed again in Lesson 5-1. Collect the cards and store them in envelopes. Name Attribute Rule Cards Tiling Surfaces with Shapes continued. Use Everything Math Deck cards to tile both a slate and a Pattern-Block Template. How many cards were needed to tile them? Slate: cards Answers vary. Pattern-Block Template: cards Answers vary. 3. Fold a sheet of paper into fourths. Cut the fourths apart. Use them to tile larger surfaces, such as a desktop. Surface Number of Fourths Answers vary. small blue shapes large red shapes large shapes, but not triangles circles, but not red Follow-Up With a partner, find things in the classroom that are tiled or covered with patterns. Make a list. Be ready to share your findings. blue and yellow shapes, but not circles red and yellow small shapes not triangles or squares large triangles, but not yellow Math Masters, page 109 Math Journal 1, p. 10 Lesson 85

5 An Attribute Rule Choose an Attribute Rule Card. Copy the rule below. Rule: Draw or describe all the attribute blocks that fit the rule. Draw or describe all the attribute blocks that do not fit the rule. These blocks fit the rule: Rules, drawings, and descriptions vary. Ongoing Learning & Practice Playing Beat the Calculator (Math Journal 1, p. 4; My Reference Book, pp. 14 and 15) PARTNER These blocks do not fit the rule: See My Reference Book, pages 14 and 15 for directions. Children play Beat the Calculator to develop their recall of addition facts. Using the Facts Power Table on journal page 4, children should record the facts for which they can beat the calculator by making a check mark in the box containing that fact. Whenever they receive three check marks for a particular fact, they can write the sum in that box to indicate they know the fact from memory. The Caller should select problems at random from the white area of the Fact Power Table. Math Journal 1, p. 103 EM3cuGMJ1_U04_80_111.indd 103 1//10 1:01 PM Ongoing Assessment: Recognizing Student Achievement Exit Slip Use an Exit Slip (Math Masters, page 415) to have children record facts from boxes in which they have at least one check mark. Children are making adequate progress if they have recorded at least half of the facts from the unshaded area. Some children will have recorded other facts. [Operations and Computation Goal 1] Math Boxes (Math Journal 1, p. 104) INDEPENDENT Name Teaching Master What s My Attribute? Work with a small group. Materials Math Journal 1, p. 103 Attribute Rule Cards (Math Masters, p. 109) scissors sheets of paper 1 set of attribute blocks: triangles, circles, squares (large and small; red, yellow, and blue) red, yellow, and blue crayons Directions 1. Cut apart the Attribute Rule Cards on Math Masters, page Mix the cards. Stack them facedown. 3. Label one sheet of paper These Fit the Rule. 4. Label another sheet These Do Not Fit the Rule. 5. Take turns being the Rule Maker. 6. The Rule Maker takes the top card from the stack. 7. The Rule Maker puts the card faceup for everyone to see. 8. Group members take turns choosing a block. Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lesson 4-5 and Lesson 4-9. The skill in Problem 6 previews Unit 5 content. Writing/Reasoning Have children draw, write, or verbalize their answers to the following: For Problem 3, explain how you know a number is even or odd. Sample answer: A number is even if it ends in, 4, 6, 8, or 0. A number is odd if it ends in 1, 3, 5, 7, or 9. Home Link (Math Masters, p. 110) INDEPENDENT Home Connection Children measure sections of a path to the nearest inch. Then they combine their measurements to find the total length of the path. Math Masters, p. 107 EM3MM_G_U04_ indd 107 1//10 9:56 AM 86 Unit 4 Addition and Subtraction

6 3 Differentiation Options ENRICHMENT Finding More Than One Way (Math Journal 1, pp. 99 and 100) PARTNER 5 15 Min To apply children s knowledge of linear measure, have them find different ways to measure the objects on journal pages 99 and 100 with a tape measure. Children should use different strategies for measuring the same length, starting at a point on the tape measure that is not the end or measuring different parts of the object and adding the results. Watch for children whose answers differ from the measurements on the journal pages. Remind children that using the ruler a different way does not change the length of an object. Name What s My Attribute? continued 9. If the block fits the rule on the card, place it on the paper that says These Fit the Rule. 10. If the block does not fit the rule, place it on the paper that says These Do Not Fit the Rule. 11. Repeat Steps 6 10 until everyone has been the Rule Maker. Follow-Up Write one of the rules on journal page 103. Draw or describe all of the blocks that fit the rule. Draw or describe all of the blocks that do not fit the rule. Try This Teaching Master Make up two rules of your own. Write them on the two blank cards given on Math Masters, page 109. Answers will vary. Sample answers: Not circles or triangles; small shapes, but not blue or red ELL SUPPORT Building a Math Word Bank (Differentiation Handbook, p. 14) SMALL-GROUP 5 15 Min Math Masters, p. 108 To provide language support for measurement concepts, use the Word Bank Template found on Differentiation Handbook, page 14. Ask children to write the terms inch and centimeter. Children describe the terms with words, pictures, and real-life examples. See the Differentiation Handbook for more information. Math Boxes Home Link Master Name HOME LINK Measuring to the Nearest Inch 1. A peach costs 15. An apple costs 1. Show the coins needed to buy both. Use Î, Â, Í, and. Sample answer: ÎÎ 3. Write even or odd on the line. 3 5 odd even even odd 5. Fill in the frames Show 67 F. 4. Write the time : 15 F 6. Use your Pattern-Block Template. Draw a hexagon. Family In today s lesson, your child measured the length, width, or height of objects to the nearest Note inch and centimeter. In later lessons, your child will make more precise measurements (such as measuring to the nearest half-inch). Ask your child to show you how to measure the sections of the path on this page. Encourage your child to measure objects in your home. Please return this Home Link to school tomorrow. 1. The ant will take this path to get to the picnic. Measure each part of the path to the nearest inch. If you do not have a ruler at home, cut out and use the ruler at the bottom of the page. picnic ant 5. What is the total length of the path? There are 6 sides Math Journal 1, p. 104 Math Masters, p. 110 Lesson 87

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