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Copyright © Wright Group/McGraw-Hill 267 Name Date Time Who Am I? HOME LINK 9 1 The problems in this Home Link involve children solving whole-number riddles. Your child will use place-value concepts, number sense, and computation skills to solve the riddles. To provide practice with basic and extended facts, multiplication fact practice is added at the bottom of this Home Link. Please return this Home Link to school tomorrow. Family Note In each riddle, I am a different whole number. Use the clues to find out who I am. 1. Clue 1:I am greater than 30 and less than 40.Who am I? Clue 2:The sum of my digits is less than 5. 2. Clue 1:I am greater than 15 and less than 40.Who am I? Clue 2:If you double me, I become a number that ends in 0. Clue 3: 1 5of me is equal to 5. 3. Clue 1:I am less than 100.Who am I? Clue 2:The sum of my digits is 4. Clue 3:Half of me is an odd number. 4. Clue 1:If you multiply me by 2, I become Who am I? a number greater than 20 and less than 40. Clue 2:If you multiply me by 6, I end in 8. Clue 3:If you multiply me by 4, I end in 2. 5. Clue 1:Double my tens digit to get Who am I? my ones digit. Clue 2:Double me and I am less than 50. Solve. 6. 8 7  7. 5 4 80 7 5 40 800 7 50 400 Practice

Copyright © Wright Group/McGraw-Hill 268 Name Date Time LESSON 9 1 Extending Multiplication Fact Patterns Fill in the missing numbers. 1. 1 10 1 100  2 10 2 100  3 10 3 100  4 10 4 100  5 10 5 100  2. 6 100 6 1,000  7 100 7 1,000  8 100 8 1,000  9 100 9 1,000  3. 1 [10] 1 [100]  2 [10s] 2 [100s]  7 [10s] 7 [100s]  5 [10s] 5 [100s]  8 [10s] 8 [100s]  4. Explain how you can use the patterns above to find the answer to 8 [1,000s]. 5. 10 100 10 [100s]  10 1,000 10 [1,000s]  Try This

Copyright © Wright Group/McGraw-Hill 269 Name Date Time Multiplication Facts and Extensions HOME LINK 92 Help your child practice multiplication facts and their extensions. Observe as your child creates fact extensions, demonstrating further understanding of multiplication. Please return this Home Link to school tomorrow. Family Note Solve each problem. 1. a. 8 [7s]  ,or 8 7  b. 8 [70s]  ,or 8 70  c. How many 8s in 56? d. How many 8s in 560? e. How many 7s in 56? f. How many 70s in 560? 2. a. 9 [7s]  ,or 9 7  b. 9 [70s]  ,or 9 70  c. How many 9s in 63? d. How many 9s in 630? e. How many 7s in 63? f. How many 70s in 630? 3. a. 8 [5s]  ,or 8 5  b. 8 [50s]  ,or 8 50  c. How many 8s in 400? d. How many 80s in 4,000? e. How many 50s in 400? f. How many 50s in 4,000? 4. Write a multiplication fact you are trying to learn. Then use your fact to write some fact extensions like those above. Multiplication Facts and Extensions HOME LINK 9 2 Help your child practice multiplication facts and their extensions. Observe as your child creates fact extensions, demonstrating further understanding of multiplication. Please return this Home Link to school tomorrow. Family Note

Copyright © Wright Group/McGraw-Hill 270 Name Date TimeName Date Time LESSON 9 2 Using Multiplication/Division Diagrams For each number story, complete the multiplication/division diagram, write a number model, and answer the question. 1. Tiffany keeps her button collection in a case with 10 shelves. On each shelf there are 16 buttons. How many buttons are in Tiffany’s collection? 2. Rashida walks her neighbor’s dog every day. She gets paid $20.00 every week. If Rashida saves her money for 30 weeks, how much money would she have? 3. The third grade class helped plant 4 tulip gardens at school. 50 tulip bulbs fit into each garden. How many tulip bulbs were planted? 4. There were 2,000 books collected in the book drive. Each class received 200 books. How many classes received books? number of shelves buttons per shelfbuttons in all number of weeksdollars per weekdollars in all number of gardensbulbs per gardenbulbs in all number of classes books per classbooks in all Number model: Answer: Number model: Answer: Number model: Answer: Number model: Answer: Try This (unit) (unit) (unit) (unit)

Copyright © Wright Group/McGraw-Hill 271 Name Date Time LESSON 9 2 Allowance Plans Sara is discussing a raise in allowance with her parents. They ask her to choose one of three plans. Plan AEach week, Sara would get 1¢ on Monday, double Monday’s amount on Tuesday, double Tuesday’s amount on Wednesday, and so on. Her allowance would keep on doubling each day through Sunday. Then she would start with 1¢ again on Monday. Plan BSara would get 32¢ on Sunday, Monday, Wednesday, and Friday of each week. She would get nothing on Tuesday, Thursday, and Saturday. Plan CSara would get 16¢ on each day of each week. Which plan should Sara choose to get the most money? Show your work on the back of this page. Explain how you found your answer. Use number sentences in your explanation. For the plan you chose, how much money would Sara earn in a year? Try This

Copyright © Wright Group/McGraw-Hill 272 LESSON 9 3 Array Multiplication Exploration A: Work in a group of three or four. Materialsarray grid (Math Masters,pp. 273 and 274, cut out and glued together) base-10 blocks (cubes and longs) red and blue crayons or coloring pencils Math Journal 2,p. 211 1. Cover a 4-by-28 array of squares on the array grid using as few base-10 blocks as you can.  Start at the lower-left corner.  First, use as many longs as you can. Then, cover the rest of the squares in your array with cubes. 2. Draw a picture of your array for Problem 1 on journal page 211.  Color the squares you covered with longs red.  Color the squares you covered with cubes blue. 3. Record the result next to the picture. 4. Now repeat Steps 1 through 3 to find the total number of squares in a 3-by-26 array. Record your work for Problem 2 on the journal page. 5. Finally, do the same for a 6-by-32 array. Record your work for Problem 3 on the journal page. Name Date Time

Copyright © Wright Group/McGraw-Hill 273 Name Date Time LESSON 9 3 Array Grid GLUE OR TAPE EDGE OF PAGE 274 HERE Start here.

Copyright © Wright Group/McGraw-Hill 274 Name Date Time LESSON 9 3 Array Grid continued

275 Name Date Time Copyright © Wright Group/McGraw-Hill LESSON 9 3 Geoboard Areas Exploration B: Work alone or with a partner. Materialsgeoboard and rubber bands, or Geoboard Dot Paper (Math Masters,p. 415) Math Journal 2,p. 212 1. On the geoboard or geoboard dot paper, make a rectangle whose area is 12 square units. Record the lengths of the longer and shorter sides in the table on journal page 212. 2. Make a different rectangle having the same area. Record the lengths of the sides in the table. 3. Repeat Steps 1 and 2 to make two different rectangles whose areas are 6 square units each. Record the lengths of the sides in the table. 4. Repeat Steps 1 and 2 to make two different rectangles (or a square and a rectangle) whose areas are 16 square units each. Record the lengths of the sides in the table. 5. Try to make a rectangle or square whose area is an odd number of square units. Record the results in your table. 6. Continue with other areas if there is time. 7. Complete journal page 212. 1 square unit

Copyright © Wright Group/McGraw-Hill 276 Name Date Time LESSON 9 3 Fractions of Fractions of Regions Exploration C: Work in a group of three or four. MaterialsMath Masters,p. 277 crayons; scissors; glue or tape You can learn a lot about fractions by folding rectangles. Each rectangle on Math Masters,page 277 is ONE. The marks on some rectangles show where to fold these rectangles into thirds, fifths, or sixths. 1. What is 1 2of 1 4? To find out, do the following: Cut out rectangle Aon Math Masters,page 277. Fold it into 4 equal parts. Each part is 1 4of the rectangle. Keep the rectangle folded. Now fold the folded rectangle in half. Each part is 1 2of 1 4of the rectangle. Unfold. How many parts are there? Color one of the parts. The colored part is 1 8of the rectangle. Complete the number model on the rectangle. 2. Repeat the same steps for rectangles Cthrough Hon Math Masters,page 277. Share the work among members of your group. Write a group report about your findings. Attach some rectangles on your report to illustrate your thinking. Answer these questions in your report: 3. Is 1 2of 1 4the same fractional part of the rectangle as 1 4of 1 2? Is 1 2of 1 3the same as 1 3of 1 2? 4. Look at the number models in the rectangles. Can you make up a rule to help you complete the number models without folding rectangles? 5. Predict 1 8of 1 2of a rectangle. Predict 1 2of 1 6. Check your predictions by folding rectangles I and J. Follow-Up

Copyright © Wright Group/McGraw-Hill 277 Name Date Time LESSON 9 3 Fractions of Fractions of Regions cont. B 1 4 1 2 of A 1 2 1 4 of C 1 2 1 3 of D 1 3 1 2 of E 12 of 15 F 1 3 1 5 of G 1 4 1 3 of H 1 4 1 5 of I 1 8 1 2 of J 1 2 1 6 of

Copyright © Wright Group/McGraw-Hill 278 Name Date Time Multiplication Number Stories HOME LINK 9 3 Your child’s class is beginning to solve multidigit multiplication and division problems. Although we have practiced multiplication and division with multiples of 10, we have been doing most of our calculating mentally. Encourage your child to explain a solution strategy for each of the problems below. Please return this Home Link to school tomorrow. Family Note 1. How many 30-pound raccoons would weigh about as much as a 210-pound harp seal? 2. How much would an alligator weigh if it weighed 10 times as much as a 50-pound sea otter? 3. How many 20-pound arctic foxes would weigh about as much as a 2,000-pound beluga whale? 4. Each porcupine weighs 30 pounds. A black bear weighs as much as 20 porcupines. How much does the black bear weigh? 5. A bottle-nosed dolphin could weigh twice as much as a 200-pound common dolphin. How much could the bottle-nosed dolphin weigh? 6. How many 2,000-pound beluga whales would weigh as much as one 120,000-pound right whale? 250 –253 Try This

Copyright © Wright Group/McGraw-Hill 279 Name Date Time LESSON 9 4 Array Multiplication 1 1. How many squares are in a 4-by-28 array? Make a picture of the array. 2. How many squares are in a 3-by-26 array? Make a picture of the array. 3. How many squares are in a 6-by-32 array? Make a picture of the array. 10 10 2 0 3 0 0 10 10 2 0 3 0 0 10 10 2 0 3 0 0 Total squares: 4 28  Total squares: 3 26  Total squares: 6 32 

Copyright © Wright Group/McGraw-Hill 280 Name Date Time The Partial-Products Algorithm HOME LINK 9 4 Today the class began working with our first formal procedure for multiplication—the partial-products algorithm. Encourage your child to explain this method to you. Please return this Home Link to school tomorrow. Family Note Use the partial-products algorithm to solve these problems: 68 69 2. 4.1. 3. 5. 75 5 85 9 31 3 Example 7 [40s]∑ 7 [6s]∑42 280 42∑ 322 46 7 280 43 6 162 7

Copyright © Wright Group/McGraw-Hill 281 Name Date Time LESSON 9 4 Base-10 Block Multiplication 1. Use longs and cubes to show 6 groups of 32. Count the number of longs. Count the number of cubes. Record your counts here: I have ten(s), which is the same as . I have one(s), which is the same as . Total: Number model: 6 32  2. Use longs and cubes to show 5 groups of 27. Count the number of longs. Count the number of cubes. Record your counts here: I have ten(s), which is the same as . I have one(s), which is the same as . Total: Number model: 5 27  3. Make up your own. Use longs and cubes to showgroups of . Count the number of longs. Count the number of cubes. Record your counts here: I have ten(s), which is the same as . I have one(s), which is the same as . Total: Number model: 

Copyright © Wright Group/McGraw-Hill 282 Name Date Time LESSON 9 4 Number Patterns 1. Suppose you were asked to find the sum of all of the whole numbers from 1 through 10. These addends make a count-by-1s pattern. A number model for this problem could look like this: 1 2 3 4 5 6 7 8 9 10  There are several ways you can find the sum. Here is one way: 1 10  2 9  3 8  4 7  5 6  How many 11s in all? The sum of the whole numbers from 1 through 10 is 11 . 2. Use the same method to find the sum in this count-by-2s pattern: 2 4 6 8 10 12 14 16 18 20  2 20 4 18 6 16  8 14 10 12  How many s in all? So the sum of the even numbers 2 through 20 is  . 3. Make up your own count-by- s pattern of addends. Then find the sum.      1 2 3 4 5 6 7 8 9 10

Copyright © Wright Group/McGraw-Hill 283 Name Date Time Saving at the Stock-Up Sale HOME LINK 9 5 Today the class used mental math and the partial-products algorithm to solve shopping problems. Note that for some of the problems below, an estimate will answer the question. For others, an exact answer is needed. If your child is able to make the calculations mentally, encourage him or her to explain the solution strategy to you. Please return this Home Link to school tomorrow. Family Note 250 – 253 191 Decide whether you will need to estimate or calculate an exact answer to solve each problem below. Then solve the problem and show what you did. Record the answer and write the number model (or models) you used. 1. Phil has $6.00. He wants to buy Creepy Creature erasers. They cost $1.05 each. If he buys more than 5, they are $0.79 each. Does he have enough money to buy 7 Creepy Creature erasers? 2. Mrs. Katz is buying cookies for a school party. The cookies cost $2.48 per dozen. If she buys more than 4 dozen, they cost $2.12 per dozen. How much are 6 dozen? Number model: 3. Baseball cards are on sale for $1.29 per card, or 5 cards for $6. Marty bought 10 cards. How much did he save with the special price? Explain how you found your answer. Number model:

Copyright © Wright Group/McGraw-Hill 284 LESSON 9 5 Dollars and Dimes Name Date Time Example:1 box of 12 Greeting Cards Price: $3.29dollars dimes Total: $ 3. 3 0 3 3 dollars dimes Total: $ dollars dimes Total: $ dollars dimes Total: $ dollars dimes Total: $ 1 roll of Gift-Wrapping Paper Price: 1 roll of Transparent Tape Price: 1 box of Tissues Price: 1 Paperback Book Price: Items to Be Purchased Dollars and Dimes Needed Use the Stock-Up Sale posters on pages 216 and 217 in your Student Reference Book.Suppose that you have only dollars and dimes. Write the least amount of money you could use to buy each item. Use dollars and dimes to help you. 193 194

Copyright © Wright Group/McGraw-Hill 285 Name Date Time LESSON 9 5 10% Sales Tax at the Stock-Up Sale You will need Math Journal 2,page 217 and your Student Reference Book. Figure out how much money Mason, Vic, and Andrea will each need if a 10% sales tax is added to their purchases.  One way to figure the 10% sales tax is to find 11 0 of the dollars and then 11 0 of the cents. Then add the amounts.  If 11 0 of the cents amount is between pennies, round to the higher amount. Example:10% of $2.43 11 0 of $2.00 is $0.20; 11 0 of $0.40 is $0.04. 11 0 of $0.03 is less than a penny so round to the higher amount, or $0.01. $0.20 $0.05 $0.25. So 10% of $2.43 is $0.25. 1. How much will Mason need for 5 bars of soap with 10% sales tax? 2. How much will Vic need for 5 toothbrushes at the sale price with 10% sales tax? 3. How much will Andrea need for 5 bottles of glue at the sale price with 10% sales tax? 194

Copyright © Wright Group/McGraw-Hill 286 Name Date Time Arrays and Factors HOME LINK 9 6 Discuss with your child all the ways to arrange 18 chairs in equal rows. Then help your child use this information to list the factors of 18 (pairs of numbers whose product is 18). Please return this Home Link to school tomorrow. Family Note Work with someone at home. The third-grade class is putting on a play. Children have invited 18 people. Gilda and Harvey are in charge of arranging the 18 chairs. They want to arrange them in rows with the same number of chairs in each row, with no chairs left over. Yes or no: If yes, Can they arrange how many chairs the chairs in … in each row? 1 row? chairs 2 rows? chairs 3 rows? chairs 4 rows? chairs 5 rows? chairs 6 rows? chairs 7 rows? chairs 8 rows? chairs 9 rows? chairs 10 rows? chairs 18 rows? chairs List all the factors of the number 18. (Hint:18 has exactly 6 factors.) How does knowing all the ways to arrange 18 chairs in equal rows help you find the factors of 18? Tell someone at home. 64– 67

Copyright © Wright Group/McGraw-Hill 287 LESSON 9 6 Name Date Time Finding Factors Materials2 different-colored counters, 2 different-colored crayons Finding Factorsgameboard (see below) Players2 Object of the GameTo shade five products in a row, column, or diagonal Directions 1. Player A places a counter on one of the factors in the Factor Strip at the bottom of the gameboard. 2. Player B places a second counter on one of the factors in the Factor Strip. (Two counters can cover the same factor.) Now that two factors are covered, Player B wins the square that is the product of the two factors. Player B shades this square with his or her color. 3. Player A moves either one of the counters to a new factor on the Factor Strip. If the product of the two covered factors has not been shaded, Player A shades this square with his or her color and wins the square. 4. Play continues until 5 squares in a row, column, or diagonal are shaded in the same color. Factor Strip 123456789 1 7 25 36 542 8 27 40 563 9 28 42 634 20 30 45 645 21 32 48 726 24 35 49 81 16 151810 1214

Copyright © Wright Group/McGraw-Hill 288 Name Date Time Sharing Money with Friends HOME LINK 9 7 In class we are thinking about division, but we have not yet introduced a procedure for division. We will work with formal division algorithms in Fourth Grade Everyday Mathematics.Encourage your child to solve the following problems in his or her own way and to explain the strategy to you. These problems provide an opportunity to develop a sense of what division means and how it works. Sometimes it helps to model problems with pennies, beans, or other counters that stand for bills and coins. Please return this Home Link to school tomorrow. Family Note 73 1. $77 is shared equally by 4 friends. a. How many $10 bills does each friend get? b. How many $1 bills does each friend get? c. How many $1 bills are left over? d. If the leftover money is shared equally, how many cents does each friend get? e. Each friend gets a total of $ . f. Number model: Practice Use the partial-products method to solve these problems. Show your work. 2. 21 3. 48 4. 63 245

Copyright © Wright Group/McGraw-Hill 289 LESSON 9 7 Name Date Time Equal Shares of Money The price of admission to the neighborhood magic show is $1.25 per person. How many people could you taketo the show ifyou had $25.00? Show your work, and explain how you figured it out. How many people could go to the show if you had $32.00? Explain your answer. Try This

Copyright © Wright Group/McGraw-Hill 290 Name Date Time Equal Shares and Equal Parts HOME LINK 9 8 As the class continues to investigate division, we are looking at remainders and what they mean. The focus of this assignment is on figuring out what to do with the remainder, NOT on using a division algorithm. Encourage your child to draw pictures, use a calculator, or use counters to solve the problems. Please return this Home Link to school tomorrow. Family Note 73 74 Solve the problems below. Remember that you will have to decide what the remainder means in order to answer the questions. You may use your calculator, counters, or pictures to help you solve the problems. 1. There are 31 children in Dante’s class. Each table in the classroom seats 4 children. How many tables are needed to seat all of the children? 2. Emily and Linnea help out on their uncle’s chicken farm. One day the hens laid a total of 85 eggs. How many cartons of a dozen eggs could they fill? 3. Ms. Jerome is buying markers for a scout project. She needs 93 markers. If markers come in packs of 10, how many packs must she buy? Practice Solve each problem using the partial-products algorithm. Use the back of this Home Link. 4. 29 4  5. 85 5  6. 96 8 

Copyright © Wright Group/McGraw-Hill 291 LESSON 9 8 Name Date Time Picturing Division For each problem— Draw a picture. Answer the question. Explain what you did with what was left over. 1. There are 18 children in art class. If 4 children can sit at each table, how many tables do they need? Picture: Answer: They need tables. Explanation: 2. Hot dogs come in packages of 8. If José is having a birthday party and needs 20 hot dogs, how many packages must he buy? Picture: Answer: He must buy packages. Explanation:

Copyright © Wright Group/McGraw-Hill 292 LESSON 9 8 Name Date Time Pizza with Remainders The third-grade class is having a pizza party. The class expects 22 children, 1 teacher, and 2 parents. Each pizza will be divided into 8 equal slices. 1. In all, how many people are coming to the party? 2. Suppose that each person who comes to the party will eat 1 slice of pizza. a. How many whole pizzas will the people eat? b. How many additional slices will be needed? c. What fractional part of a whole pizza is that? d. Is that more or less than half of a whole pizza? e. How many whole pizzas should the teacher order? 3. Suppose instead that each person will eat 2 slices of pizza. a. How many slices of pizza will the people eat? b. How many whole pizzas will the people eat? c. How many additional slices will be needed? d. What fractional part of a whole pizza is that? e. How many whole pizzas should the teacher order? 4. Lakeisha brought 2 granola bars to the party. She decided to share them equally with her 3 best friends. What fractional part of a granola bar did she and her friends get?

Copyright © Wright Group/McGraw-Hill 293 Name Date Time Multiplication Two Ways, Part 1 HOME LINK 9 9 Observe as your child solves these problems. See if your child can use more than one method of multiplication, and find out which method your child prefers. Both methods are discussed in the Student Reference Bookon pages 68–72 and in the Unit 9 Family Letter. Please return this Home Link to school tomorrow. Family Note 68–72 Use the lattice method and the partial-products algorithm. 1. 2 46  3. 3 274  2. 5 83  4. 8 906  46 283 5 274  3906 8 2 4 6 5 8 3 3 2 7 4

Copyright © Wright Group/McGraw-Hill 294 LESSON 9 9 Name Date Time Mathematics in Music The French composer Erik Satie lived from 1866 to 1925. He wrote a piece of music called Vexations,in which the same tune is played 840 times in a row without stopping. It takes about 30 seconds to play this tune once. 1. About how many minutes would it take to play all of Vexationswithout stopping? about minutes 2. How many hours is that? hours 3. Suppose someone played the whole piece 4 times without stopping. Could this be done in 1 day? 4. How many times a day could the whole piece be played without stopping? 5. Look up the meaning of vexationin a dictionary. Explain why you think Satie gave the piece of music that name.

Copyright © Wright Group/McGraw-Hill 295 LESSON 9 10 Name Date Time Array Multiplication 2 Exploration D: Work in a group of 2 to 4. Materialsarray grid base-10 blocks (at least 3 flats and 24 longs) Math Journal 2,p. 229 green and red crayons or coloring pencils 1. Cover a 20-by-13 array of squares on the array grid using as few base-10 blocks as possible.  Start at the lower-left corner.  Use flats first and then longs. 2. Make a picture of this array in Problem 1 on journal page 229.  Color the squares covered by flats green.  Color the squares covered by longs red. 3. Record the result next to the picture. 4. Cover an 18-by-30 array of squares on the array grid using as few base-10 blocks as possible.  Start at the lower-left corner.  Use flats first and then longs. 5. Make a picture of this array in Problem 2 on journal page 229.  Color the squares covered by flats green.  Color the squares covered by longs red. 6. Record the result next to the picture.

Copyright © Wright Group/McGraw-Hill 296 LESSON 9 10 Name Date Time Array Multiplication 3 Exploration D: continued Work in a group of 2 to 4. Materialsarray grid base-10 blocks (at least 4 flats, 25 longs, and 28 cubes) Math Journal 2,p. 230 green, red, and blue crayons or coloring pencils 1. Cover a 17-by-34 array of squares on the array grid using as few base-10 blocks as possible.  Start at the lower-left corner.  Use flats first, and then longs, and finally cubes. 2. Make a picture of this array in Problem 1 on journal page 230.  Color the squares covered by flats green.  Color the squares covered by longs red.  Color the squares covered by cubes blue. 3. Record the result next to the picture. 4. Cover a 22-by-28 array of squares on the array grid using as few base-10 blocks as possible.  Start at the lower-left corner.  Use flats first, and then longs, and finally cubes. 5. Make a picture of this array in Problem 2 on journal page 230.  Color the squares covered by flats green.  Color the squares covered by longs red.  Color the squares covered by cubes blue. 6. Record the result next to the picture.

Copyright © Wright Group/McGraw-Hill 297 LESSON 9 10 Name Date Time Equilateral Triangles Exploration E: MaterialsMath Masters,pp. 298 and 299 triangle pattern blocks Pattern-Block Template blank paper (optional) Problem How many triangle pattern blocks will fit inside each of the triangles on Math Masters, page 299? All of the triangles on Math Masters,page 299 are equilateral triangles. The sides of each triangle are all the same length. The smallest triangle is 1 inch on each side. The sides of each of the other triangles are also drawn to the whole inch. Work with a partner or a small group. Follow the steps below. Share ideas about ways to find solutions and complete the table. 1. How many 1-inch triangles fit inside the 2-inch triangle? You may use pattern blocks to find out. Record your answer in the table on Math Masters,page 298. 2. How many 1-inch triangles fit inside the 3-inch triangle? Record your answer in the table. Hint: A part of the 3-inch triangle is a 2-inch triangle. 3. Look for a pattern. Predict how many 1-inch triangles will fit inside the 4-inch triangle. Check your prediction with pattern blocks. Record and compare your answer to your prediction. Repeat for the 5-inch triangle. 4. Predict how many 1-inch triangles will fit in 6-inch through 10-inch triangles. Build or draw each triangle with pattern blocks or by tracing shapes from the Pattern-Block Template onto blank paper. Record and compare your predictions with your answers. 5. Look at the table with others in your group. Discuss the number pattern in the answers. Together decide on ways to describe the pattern. Write your description of the pattern below your table.

Copyright © Wright Group/McGraw-Hill 298 LESSON 9 10 Name Date Time Equilateral Triangles continued 1 1 2345678910 Length of each side in inches Number of 1-in. triangles inside Describe number patterns that you see in the table. Exploration E: continued Fill in the table.

Copyright © Wright Group/McGraw-Hill 299 Name Date Time LESSON 9 10 Equilateral Triangles continued Exploration E: continued

Copyright © Wright Group/McGraw-Hill 300 LESSON 9 10 Name Date Time Building Bridges Exploration F: Work alone or with a partner. Materials8 1 2-by-11 sheet of papercentimeter ruler; scissors 2 equal-size bookspaper for recording light objects—paper clips, rubber bands, straws, pencils, crayons, erasers, calculators, and so on 1. Fold the paper into fourths as shown. Cut along the folds. 2. Make a bridge between two books with one of the rectangles as shown. This is Bridge #1. Check to see if this bridge will hold any of the light objects. Record what you find. 3. Fold another rectangle into 8 or 9 equal-size fan-folds as shown. This will make the folds a little more than 1 cm apart. This is Bridge #2. Place it between the two books. Test the bridge by placing light objects, and then heavier objects, on it. Record the objects this bridge can hold. 4. Fold another rectangle into 12 to 14 equal-size folds (each a little more than 1 2centimeter apart). This is Bridge #3. Test what thisbridge can hold. Record your results. Compare your results with results of other members of the class. Discuss these questions. Record your thoughts on a piece of paper.  Do the sizes of the folds affect how much the bridge holds?  What shapes do you see in the fan-folded rectangles?  Why are the fan-folded bridges able to hold up more than the unfolded bridge? Bridge #1 Fan-folded Rectangle Bridge #2 Practice

Copyright © Wright Group/McGraw-Hill 301 Name Date Time Multiplication Two Ways, Part 2 HOME LINK 9 10 The class continues to practice the partial-products algorithm and the lattice method. Encourage your child to try these problems both ways and to compare the answers to be sure they are correct. Please return this Home Link to school tomorrow. Family Note 68–72 Show someone at home how to use both the lattice method and the partial-products algorithm. 57 391 4 480 9 3 5 7 4 9 1 8 2 0 4 204 8 1. 3 57  3. 8 204  2. 4 91  4. 9 480 

Copyright © Wright Group/McGraw-Hill 302 LESSON 9 10 Name Date Time Triangular Numbers 1. How many dots are in each of the triangular arrays? List the number of dots on the line below each triangular array. These are triangular numbers. What patterns do you see? 2. Show the tenth triangular number. How many dots are in the triangular array? Explain how you figured it out. 1

Copyright © Wright Group/McGraw-Hill 303 LESSON 9 11 Name Date Time 1. How many squares are in a 20-by-13 array? Total squares  20 13  2. How many squares are in an 18-by-30 array? Total squares  18 30  20 10 0 10 20 10 20 0 10 20 30 Array Multiplication 4

Copyright © Wright Group/McGraw-Hill 304 Name Date Time 2-Digit Multiplication: Two Ways HOME LINK 9 11 Your child’s class continues to practice the partial-products algorithm and the lattice method, now with 2-digit numbers and 2-digit multiples of 10. Please return this Home Link to school tomorrow. Family Note 68–72 Use the lattice method and the partial-products algorithm. On the back of this page, use your favorite method to solve these problems. 4. 40 28  5. 60 35  1. 20 38  2. 50 17  3. 90 62  8 2 3 0 Practice

Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill 305 305 LESSON 9 11 Name Date Time An Error in Lattice Multiplication There is a mistake in the following problem. Circle the mistake, and describe it in words. 1. Mistake: 9 3 9 2 0 0 2 7 7 2 0 61 2 6 2 8 LESSON 9 11 Name Date Time An Error in Lattice Multiplication There is a mistake in the following problem. Circle the mistake, and describe it in words. 1. Mistake: 9 3 9 2 0 0 2 7 7 2 0 61 2 6 2 8

Copyright © Wright Group/McGraw-Hill 306 Name Date Time 1. How many squares are in a 17-by-34 array? Total squares  17 34  2. How many squares are in a 22-by-28 array? Total squares  22 28  20 10 0 10 20 30 20 10 0 10 2030 LESSON 9 12 Array Multiplication 5

Copyright © Wright Group/McGraw-Hill 307 Name Date Time 2 Digits 2 Digits HOME LINK 9 12 The class continues to practice the partial-products algorithm and the lattice method, now with any 2-digit numbers. Encourage your child to try these problems both ways and to compare the answers to be sure they are correct. Please return this Home Link to school tomorrow. Family Note 68–72 Use the lattice method and the partial-products algorithm. On the back of this page, use your favorite method to solve these problems. 4. 55 49  5. 91 33  1. 21 35  2. 17 43  3. 58 62  5 2 3 1 Practice

Copyright © Wright Group/McGraw-Hill 308 LESSON 9 12 Name Date Time Egyptian Multiplication With a partner, carefully study the Egyptian multiplication algorithm below. Then solve a problem using this method. Example:13 28 Step 1:Write the first factor in the first column (13). Then write 1 in the first row below the factor. Double 1 and write 2 in therow below. Continue to double the number above until you get a number that is equal to or greater than the first factor. Cross out that number if it is greater than the first factor. 16 is crossed out. Step 2:Write the second factor in the second column (28). Then write that number again in the box below. (It should be next to the 1 in the first column.) Double that number in each new line until the last number lines up with the last number of the first column (224 lines up with 8). Step 3:Starting with the greatest number in column 1 (8), circle the numbers that add up to be the first factor (13). 8 4 1 13 Cross out the row of numbers that you did not use to make the first factor (2 and 56). Step 4:Add the numbers in the second column that are not crossed out. 28 112 224 364 Answer:13 28 364 Check the answer by solving the problem using an algorithm you already know. 1st factor: 2 nd factor: 13 1 2 4 8 16 1st factor: 2 nd factor: 13 28 128 256 4112 8224 16 1st factor: 2 nd factor: 13 28 128 2 56 4112 8224 16 1st factor:2 nd factor: 13 28 128 2 56 4112 8224 16

Copyright © Wright Group/McGraw-Hill 309 LESSON 9 12 Name Date Time Egyptian Multiplication continued Work with a partner to solve each problem following the steps of the Egyptian algorithm. Check your answers by solving the problems using an algorithm you already know. 1. 24 32 Answer: 24 32  Do your own. 2.  Answer:   1st factor: 2 nd factor: Try This 1st factor: 2 nd factor: 24

Copyright © Wright Group/McGraw-Hill 310 LESSON 9 12 Name Date Time Lattice Grids (2-Digit3-Digit)

Copyright © Wright Group/McGraw-Hill 311 LESSON 9 12 Name Date Time Lattice Grids (2-Digit2-Digit)

Copyright © Wright Group/McGraw-Hill 000 000 312 Name Date Time HOME LINK 9 13 Encourage your child to use the thermometer pictured here to answer questions about thermometer scales, temperature changes, and temperature comparisons. If you have a real thermometer, try to show your child how the mercury moves up and down. Please return this Home Link to school tomorrow. Family Note 170 –173 1. What is the coldest temperature this thermometer could show? a. °F b. °C 2. What is the warmest temperature this thermometer could show? a. F b. C 3. What temperature is 20 degrees warmer than 10C? 4. How much colder is 9C than 9C? 5. Would 30C be a good temperature for swimming outside? For sledding? Explain. 6. Would 6C be a good temperature for ice-skating? For in–line skating? Explain. Positive and Negative Temperatures ° F –40–30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 ° C 60 70 80 90 100 50 40 30 20 10 0 –10 –20 –30 –40 Water boils Body Temperature Room Temperature Water freezes Salt solution freezes

Copyright © Wright Group/McGraw-Hill 313 LESSON 9 13 Name Date Time Negative Numbers on a Number Line Show the jumps on the number lines. 1. Start at 10. Count back 13. Where did you land? 2. Start at 15. Count up 22. Where did you land? 3. Start at 40. Count back 50. Where did you land? 4. Do your own. Start at . Count . Where did you land? 5. Describe the relationships you see between the three numbers in each problem. 20100 1020304050 20100 1020304050 20100 1020304050 20100 1020304050 Try This

Copyright © Wright Group/McGraw-Hill 314 LESSON 9 13 Name Date Time Exploring Order in Subtraction You will need number cards 0–10 (2 of each).  Place the cards number-side down.  Choose 2 cards. Record the numbers in the chart below.  Write 2 subtraction number sentences in the table, one in which the larger number is written first and one in which the smaller number is written first. Use the number line at the bottom of this page to help you figure out the differences.  Follow the steps 3 more times. 1. Look at the number sentences you wrote. Does the order of numbers in a subtraction number sentence matter? 2. How do you know? 10987654321012345678910 Numbers on Number Cards Sentences Example 4, 66-4=2 4-6=-2 1__  __  __ __  __  __ 2__  __  __ __  __  __ 3__  __  __ __  __  __ 4__  __  __ __  __  __

315 Copyright © Wright Group/McGraw-Hill Name Date Time Unit 10: Family Letter HOME LINK 9 14 Measurement and Data This unit has three main objectives:  To review and extend previous work with measures of length, weight, and c\ apacity by providing a variety of hands-on activities and applications. These activ\ ities will provide children with experience using U.S. customary and metric units of measurement.  To extend previous work with the median and mode of a set of data and to \ introduce the mean (average) of a set of data.  To introduce two new topics: finding the volume of rectangular prisms and\ using ordered pairs to locate points on a coordinate grid. Children will repeat the personal measurements they made earlier in the \ year so that they may record their own growth. They will display these data in graphs and \ tables and find typical values for the class by finding the median, mean, and mode of th\ e data. They will begin to work with volumes of rectangular boxes, which have re\ gular shapes, and will also compare the volumes of several irregular objects and inves\ tigate whether there is a relationship between the weight of these objects and their vo\ lumes. Please keep this Family Letter for reference as your child works through Unit 10. 1 kilometer 1,000 meters 1 meter 100 centimeters 1 centimeter 10 millimeters 1 mile 1,760 yards 1 yard 3 feet 1 foot 12 inches 1 kilogram 1,000 grams 1 gram 1,000 milligrams 1 ton 2,000 pounds 1 pound 16 ounces 1 liter 1,000 milliliters 1 gallon 4 quarts 1 quart 2 pints 1 pint 2 cups 1 cubic yard = 27 cubic feet 1 cubic foot = 1,728 cubic inches Tables of Measures Length Weight Volume & Capacity

Copyright © Wright Group/McGraw-Hill 316 HOME LINK 914 Unit 10: Family Letter cont. coordinate grid A reference frame for locating points in a plane by means of ordered pairs of numbers. A rectangular coordinate grid is formed by two number lines that intersect at right angles at their zero points. coordinate A number used to locate a point on a number line; a point’s distance from an origin. ordered number pair A pair of numbers used to locate a point on a coordinate grid. height of a prism The length of the shortest line segment from a base of a prism to the plane containing the opposite face. The height is perpendicular to the base. volume The amount of space occupied by a 3-dimensional shape. square centimeter (square cm, cm 2) A unit to measure area. For example, a square centimeter is the area of a square with 1-cm long sides. cubic centimeter (cubic cm, cm 3) A metric unit of volume or capacity equal to the volume of a cube with 1cm edges. weight A measure of how heavy something is; the force of gravity on an object. capacity (of a scale) The maximum weight a scale can measure. For example, most infant scales have a capacity of about 25 pounds. capacity (of a container) The amount a container can hold. Capacity is often measured in units such as quarts, gallons, cups, or liters. frequency table A table in which data are tallied and organized, often as a first step toward making a frequency graph. mode The value or values that occur most often in a set of data. For example, in the frequency table above, 30 inches is the mode. mean The sum of a set of numbers divided by the number of numbers in the set. Often called the average value of the set. Vocabulary Important terms in Unit 10: 3 2 1 01 Coordinate grid23 (3,3) ordered number pair coordinates Fr e q u e n c y Ta l l i e s N u m b e r 27 // 2 28 0 29 ////\5 30 ////\ /// 8 31 ////\ // 7 32 //// 4 To t a l 26 Waist- to- floor mea s u rement (i n c h e s)

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