Name. 4. Lilly completed a math project worth 200 points. She earned all but 13 points. How many points did she earn?

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1 Daily Spiral Review The model is shaded to represent a fraction. Which model below shows an equivalent fraction? A B C D 2. Jimmy s basketball team scored 35 points in the last game. There are 7 members on the team, and each member scored the same number of points. How many points did each member score? A 7 B 6 C 5 D 4 4. Lilly completed a math project worth 200 points. She earned all but 13 points. How many points did she earn? 5. Thomas owns 12 books. If he buys enough books to double his collection and then loans out half of his books, how many books does he have left? 6. Write out the following number: Thirty-six million, eight hundred sixty thousand, nine hundred fifty-two. 7. Complete the following pattern: 9, 18, 27, 36,,, Daily Spiral Review On Saturday night, 234 people attended the school play. Admission to the play was $4. How much money did the school collect by charging admission? A $932 B $936 C $938 D $940 Topic 6 15

2 Daily Spiral Review The model is shaded to represent a fraction. Which model below shows an equivalent fraction? A B C D 2. Jimmy s basketball team scored 35 points in the last game. There are 7 members on the team, and each member scored the same number of points. How many points did each member score? A 7 B 6 C 5 D 4 4. Lilly completed a math project worth 200 points. She earned all but 13 points. How many points did she earn? 187 points 5. Thomas owns 12 books. If he buys enough books to double his collection and then loans out half of his books, how many books does he have left? 12 books 6. Write out the following number: Thirty-six million, eight hundred sixty thousand, nine hundred fifty-two. 36,860, Complete the following pattern: , 18, 27, 36,,, Daily Spiral Review On Saturday night, 234 people attended the school play. Admission to the play was $4. How much money did the school collect by charging admission? A $932 B $936 C $938 D $940 Topic 6 15

3 16 Topic 6 Problem of the Day Problem of the Day Write an equation and find its value. Roger found 6 shells. Tom found 8 more shells than Roger. How many shells did Tom find? Problem of the Day 6-1

4 Quick Check Which number sentence would you need to solve in order to find the missing number? x x A 70 7 B 78 7 C D 78 7 Quick Check What is the missing value? p p A 10 B 11 C 12 D Writing to Explain Explain how you would find the missing values in the table. k k 4 Topic 6 17

5 Quick Check Which number sentence would you need to solve in order to find the missing number? x x A 70 7 B 78 7 C D 78 7 Quick Check What is the missing value? p p A 10 B 11 C 12 D Writing to Explain Explain how you would find the missing values in the table. k k 4 See student samples to the right. Topic 6 17

6 Variables and Expressions Reteaching 6-1 Reteaching 6-1 How do you use expressions containing variables? To use an expression with a variable, replace the variable with a value and compute. Suppose n 6. Substitute 6 for n. Then, add. 36 n You can also use a table. t t Substitute 35 for the expression t The missing number is 20. Copy and complete the table. w w Number Sense Does the expression d 12 have a greater value when d 42 or when d 46? Find the missing number in each table. 5. e e g g Topic 6

7 Variables and Expressions Reteaching 6-1 Reteaching 6-1 How do you use expressions containing variables? To use an expression with a variable, replace the variable with a value and compute. Suppose n 6. Substitute 6 for n. Then, add. 36 n You can also use a table. t t Substitute 35 for the expression t The missing number is 20. Copy and complete the table. w w Number Sense Does the expression d 12 have a greater value when d 42 or when d 46? Find the missing number in each table. 5. e e When d 46 g g Topic 6

8 Variables and Expressions Copy and complete the table. Practice 6-1 k k ! ! 3. 11! ! 7 91 Complete the table for each problem x x b b Practice z z y y When c = 4, what is the value of the expression 72 c? A 18 B 20 C 24 D Writing to Explain Explain how you could show five less than a number using an expression. Topic 6 19

9 Variables and Expressions Copy and complete the table. Practice 6-1 k k ! ! 3. 11! ! Complete the table for each problem x x b b Practice z z y y When c = 4, what is the value of the expression 72 c? A 18 B 20 C 24 D Writing to Explain Explain how you could show five less than a number using an expression. Sample answer: Assign the variable n to represent any number, and show the expression n 5. Topic 6 19

10 Enrichment 6-1 Name Who Wants Pizza? Use the pizza menu to answer the questions below. 1. Alexandra has $ She wants enough pizza to feed 8 people. What should she order? Order No. Pizza Sizes Roger s Pizza Enrichment 6-1 Decision Making Number of People Price 1 2 small pizzas 4 $ large, 1 small 5 $ large 3 $ small 2 $ Carlos is buying lunch for himself. What should he get? 3. Julia is paying for order No. 2. Should she use a $10.00 bill or a $20.00 bill? 4. André pays for order No. 1 with a $20.00 bill. How much change will he get back? 5. On each table at the pizza restaurant is the sign at the right. Bill ordered a small pizza with extra cheese. Cynthia, Derek, and Juanita ordered a large pizza. Who will eat first? How Long It Takes to Cook Small Pizza Large Pizza Any pizza with extra cheese 20 min 30 min Add 10 min 20 Topic 6

11 Enrichment 6-1 Name Who Wants Pizza? Use the pizza menu to answer the questions below. 1. Alexandra has $ She wants enough pizza to feed 8 people. What should she order? Alexandra should get two orders of No. 1. Order No. Pizza Sizes Roger s Pizza Enrichment 6-1 Decision Making Number of People Price 1 2 small pizzas 4 $ large, 1 small 5 $ large 3 $ small 2 $ Carlos is buying lunch for himself. What should he get? Carlos should get order No Julia is paying for order No. 2. Should she use a $10.00 bill or a $20.00 bill? Julia should pay with a $20.00 bill. 4. André pays for order No. 1 with a $20.00 bill. How much change will he get back? André will get $11.05 in change. 5. On each table at the pizza restaurant is the sign at the right. Bill ordered a small pizza with extra cheese. Cynthia, Derek, and Juanita ordered a large pizza. Who will eat first? They will all eat at the same time. How Long It Takes to Cook Small Pizza Large Pizza Any pizza with extra cheese 20 min 30 min Add 10 min 20 Topic 6

12 Daily Spiral Review 6-2 Students at Wood Elementary School participated in a Penny Challenge. Ms. Brenner s class used the chart below to keep track of the amount of money they raised each day. Day Amount of Money Monday $4.74 Tuesday $6.23 Wednesday $11.78 Thursday $9.55 Friday $12.49 Use the chart to answer questions 1 and What is the total amount of money Ms. Brenner s class raised? A $42.79 B $44.79 C $44.99 D $ Annie tutors 8 students each week. She charges each student $72 a week. About how much money does Annie earn each week? 4. In the number 34,278,915, give the place values of the following numbers: 7: 9: 5: 5. Complete the table. k k Daily Spiral Review What is the difference between the amount Ms. Brenner s class raised on Friday and the amount they raised on Monday? A $7.75 B $8.75 C $16.23 D $ What fraction is modeled by the shaded area below? Write your answer in simplest form. Topic 6 21

13 Daily Spiral Review 6-2 Students at Wood Elementary School participated in a Penny Challenge. Ms. Brenner s class used the chart below to keep track of the amount of money they raised each day. Day Amount of Money Monday $4.74 Tuesday $6.23 Wednesday $11.78 Thursday $9.55 Friday $12.49 Use the chart to answer questions 1 and What is the total amount of money Ms. Brenner s class raised? A $42.79 B $44.79 C $44.99 D $ What is the difference between the amount Ms. Brenner s class raised on Friday and the amount they raised on Monday? A $7.75 B $8.75 C $16.23 D $ Annie tutors 8 students each week. She charges each student $72 a week. About how much money does Annie earn each week? $ In the number 34,278,915, give the place values of the following numbers: ten thousands hundreds ones 7: 9: 5: 5. Complete the table. k k What fraction is modeled by the shaded area below? Write your answer in simplest form. Daily Spiral Review Topic 6 21

14 22 Topic 6 Problem of the Day Problem of the Day Write a number expression and then give its value. On the first day in September, Antonio had $134 in his savings account. On the first day in October, Antonio had $201 in his savings account. How much money did Antonio save in September? Problem of the Day 6-2

15 Quick Check What is a rule for this table? x What is a rule for this table? p A x 6 B x 6 C x 7 D x 7 A p 19 B p 22 C p 22 D p Writing to Explain Juliet s Book Shop is having a sale. What expression can Juliet write to figure out sale prices? Explain how you found the expression. Then, use the expression to find the sale prices on $30, $35, and $40. Quick Check 6-2 Regular Price (p) $10 $15 $20 $25 $30 $35 $40 Sale Price $8 $13 $18 $23 Topic 6 23

16 Quick Check What is a rule for this table? x What is a rule for this table? p A x 6 B x 6 C x 7 D x 7 A p 19 B p 22 C p 22 D p Writing to Explain Juliet s Book Shop is having a sale. What expression can Juliet write to figure out sale prices? Explain how you found the expression. Then, use the expression to find the sale prices on $30, $35, and $40. Quick Check 6-2 Regular Price (p) $10 $15 $20 $25 $30 $35 $40 Sale Price $8 $13 $18 $23 See student samples to the right. Topic 6 23

17 Addition and Subtraction Expressions Reteaching 6-2 How do you find a rule to write an expression? To find a rule and write an expression, look at the numbers being compared. Which is the greater number? v Reteaching 6-2 Consider 57 and is greater than 50, so rule out addition. Find how much greater 57 is than is 7 more than 50, so the rule must involve subtraction. Compare the numbers in each column of the table. Look at the other two columns of numbers and compare them. The top number is 7 more than the bottom number. A rule is subtract 7, so the expression is v 7. Find a rule for each table r f Find a rule and write the missing number for each table c h m s Topic 6

18 Addition and Subtraction Expressions Reteaching 6-2 How do you find a rule to write an expression? To find a rule and write an expression, look at the numbers being compared. Which is the greater number? v Reteaching 6-2 Consider 57 and is greater than 50, so rule out addition. Find how much greater 57 is than is 7 more than 50, so the rule must involve subtraction. Compare the numbers in each column of the table. Look at the other two columns of numbers and compare them. The top number is 7 more than the bottom number. A rule is subtract 7, so the expression is v 7. Find a rule for each table. 1. r f 4 r f Find a rule and write the missing number for each table. 3. c h 8 c h m 43 s 17 m s Topic 6

19 Addition and Subtraction Expressions Practice 6-2 Find a rule and write the missing number for each table r a s b Practice 6-2 w n Evaluate the expression 15 n when n Which expression stands for 32 more than a number d? A 32 d B 32 d C 32 d D 32 d 9. Writing to Explain Explain how you know to use a variable in an addition or subtraction expression. Topic 6 25

20 Addition and Subtraction Expressions Find a rule and write the missing number for each table. 1. r a 34 r w a s 5 4. b 16 s b w 3 6. n Practice 6-2 n Practice Evaluate the expression 15 n when n Which expression stands for 32 more than a number d? A 32 d B 32 d C 32 d D 32 d 9. Writing to Explain Explain how you know to use a variable in an addition or subtraction expression. Sample answer: You use a variable to represent an unknown value in an expression. 6 Topic 6 25

21 Algebra Cadabra! Find the value for x in the following exercises. Enrichment 6-2 Algebra 1. x 7 x x x 6 15 Enrichment x x x x x x x x 5 x x x x x 11 x x x x x x x x x x 6 x 4 x 9 x x 4 x x 5 x x x x 5 x 8 x x x x x x x x x x x Topic 6

22 Enrichment 6-2 Algebra Cadabra! Find the value for x in the following exercises. 1. x 7 x x x x x x x x x x x 5 x x x x x 11 x x x x x x x x x x 6 x 4 x 9 x x 4 x x 5 x x x x 5 x 8 x x x x x x x x x x x Enrichment 6-2 Algebra 26 Topic 6

23 Daily Spiral Review In standard form, what is four hundred two thousand, nine hundred eighty-one? A 42,981 B 402,981 C 420,981 D 429, The parents of 4th-grade students at Mulcahey School were invited to attend an open house. The parents were put into 6 equal groups. Each group had 31 parents. How many parents attended the open house? A 25 B 37 C 180 D Willow bought a backpack that cost $ She paid for it with a $20 bill. How much change did she get? 5. Round the number to the following places: Tenths: Hundredths: Whole Number: 6. There are 24 students in Mrs. McGovern s class, and only half of them returned their permission slip on time. How many students returned their permission slip on time? Daily Spiral Review Brian s dad drives 32 miles to work. If he makes the trip 2 times a day, how many miles does he travel each day? A 64 B 60 C 54 D Complete the following pattern: 96, 84, 72, 60,,, Topic 6 27

24 Daily Spiral Review In standard form, what is four hundred two thousand, nine hundred eighty-one? A 42,981 B 402,981 C 420,981 D 429, The parents of 4th-grade students at Mulcahey School were invited to attend an open house. The parents were put into 6 equal groups. Each group had 31 parents. How many parents attended the open house? A 25 B 37 C 180 D Brian s dad drives 32 miles to work. If he makes the trip 2 times a day, how many miles does he travel each day? A 64 B 60 C 54 D Willow bought a backpack that cost $ She paid for it with a $20 bill. How much change did she get? $ Round the number to the following places: Tenths: Hundredths: Whole Number: 6. There are 24 students in Mrs. McGovern s class, and only half of them returned their permission slip on time. How many students returned their permission slip on time? Complete the following pattern: , 84, 72, 60,,, Daily Spiral Review 6-3 Topic 6 27

25 Problem of the Day Topic 6 Problem of the Day 6-3 Jo spent $18. Copy and complete the table to show how much she had left if she started with d dollars. d d Problem of the Day 6-3

26 1. What is a rule for the table? s A s 28 B s 5 C s 5 D s 7 Quick Check What is a rule for the table? g A g + 15 B g 6 C g 6 D g Writing to Explain The Ramirez family s favorite snack is yogurt. Mrs. Ramirez buys yogurt in different-sized cases. Number of containers in a case How many days pass before it is all eaten Quick Check 6-3 How many days would pass before a case of 25 yogurts was all eaten? Explain your reasoning. Topic 6 29

27 1. What is a rule for the table? s A s 28 B s 5 C s 5 D s 7 Quick Check What is a rule for the table? g A g + 15 B g 6 C g 6 D g Writing to Explain The Ramirez family s favorite snack is yogurt. Mrs. Ramirez buys yogurt in different-sized cases. Number of containers in a case How many days pass before it is all eaten Quick Check 6-3 How many days would pass before a case of 25 yogurts was all eaten? Explain your reasoning. See student samples to the right. Topic 6 29

28 Multiplication and Division Expressions Reteaching 6-3 Find a rule and write an expression using multiplication and division. To find a rule and write an expression, look at the numbers being compared. Which is the greater number? b Reteaching 6-3 Consider 3 and is greater than 3, so rule out subtraction and division. Find how much greater 24 is than is 8 times more than 3, so the rule must involve multiplication. Look at the other two columns of numbers and compare them. The bottom number is 8 times more than the top number. Compare the numbers in each column of the table. A rule is multiply by 8, so the expression is 8 b. Find a rule for each table a u Find a rule and write the missing number for each table j e p q Topic 6

29 Multiplication and Division Expressions Reteaching 6-3 Find a rule and write an expression using multiplication and division. To find a rule and write an expression, look at the numbers being compared. Which is the greater number? b Reteaching 6-3 Consider 3 and is greater than 3, so rule out subtraction and division. Find how much greater 24 is than is 8 times more than 3, so the rule must involve multiplication. Look at the other two columns of numbers and compare them. The bottom number is 8 times more than the top number. Compare the numbers in each column of the table. A rule is multiply by 8, so the expression is 8 b. Find a rule for each table. 1. a 8 2. u 4 a u Find a rule and write the missing number for each table j 2 j p p e 14 e q q Topic 6

30 Multiplication and Division Expressions Find a rule and write the missing number for each table Practice 6-3 m k z q e l Practice Evaluate the expression 48 n when n Which expression means 3 times a number h? A 3 h B 3 h C 3 h D 3 h 9. Writing to Explain How could you show the inverse operation of Exercise 5 above? Topic 6 31

31 Multiplication and Division Expressions Find a rule and write the missing number for each table m 9 m z z e e Evaluate the expression 48 n when n k 7 8. Which expression means 3 times a number h? k q q l l A 3 h B 3 h C 3 h D 3 h 8 Practice Practice Writing to Explain How could you show the inverse operation of Exercise 5 above? Sample answer: Invert the table and change the rule to e 6. Topic 6 31

32 Very Variable 1. A $1 bill represents 100 cents. The value of a dollar could also be represented by dimes. Divide the picture of the dollar to represent dimes. Complete the expression for the number of dimes in 100 cents where d is equal to 10 cents, the value of a dime. Enrichment 6-3 Algebra $1 100 d dimes d Enrichment The length of the Oregon Trail was about 2,000 miles long. This route would take settlers 4 months to travel. Use n, the number of miles traveled per month, to write a multiplication expression that represents the total distance traveled. What is the value of n? Three students are playing a math game. Each student gives a value for the variable in the expression and then evaluates the expression. The student with the greatest value wins the round. The students variable values are given in the table. Student Value Bobby 10 Hannah 2 Carlos 4 3. The first expression is (3 7) (n 2 10). Who wins the round? What is the value of the expression? 4. The next expression is (3n + 2) 2. Who wins the round? What is the value of the expression? 32 Topic 6

33 Very Variable 1. A $1 bill represents 100 cents. The value of a dollar could also be represented by dimes. Divide the picture of the dollar to represent dimes. Complete the expression for the number of dimes in 100 cents where d is equal to 10 cents, the value of a dime. $ d dimes Enrichment 6-3 Algebra d Enrichment The length of the Oregon Trail was about 2,000 miles long. This route would take settlers 4 months to travel. Use n, the number of miles traveled per month, to write a multiplication expression that represents the total distance traveled. What is the value of n? 4n; 4n 2,000; 2, ; n 500 Three students are playing a math game. Each student gives a value for the variable in the expression and then evaluates the expression. The student with the greatest value wins the round. The students variable values are given in the table. Student Value Bobby 10 Hannah 2 Carlos 4 3. The first expression is (3 7) (n 2 10). Who wins the round? What is the value of the expression? Hannah wins with 90; Bobby: 50; Carlos: The next expression is (3n + 2) 2. Who wins the round? What is the value of the expression? Bobby wins with 16; Hannah: 4; Carlos: 7 32 Topic 6

34 Daily Spiral Review Bill and Ron each ate part of a candy bar. The models below are shaded to show the part that each boy had left. 3. Order the following numbers from greatest to least: 180, 108, 118, 181 Which of the following compares the portions of candy bars that were left? A B C D The first clock below shows when Shane arrived at the library. The second clock shows when he left. How much time did Shane spend at the library? A.M. P.M. 4. Mrs. Bird s class baked 45 cupcakes for the fundraiser. They sold 23 cupcakes. Write the number sentence that tells how many cupcakes were NOT sold. 5. Keisha bicycles 18 kilometers each day. If she cycles the same distance each day, how far does she cycle in 7 days? 6. Raul and Mischa measure the same wall. Raul says it is 60 inches long. Mischa says it is 5 feet long. Explain how they can both be right. Daily Spiral Review 6-4 to A 4 hours B 4 hours 30 minutes C 5 hours D 5 hours 30 minutes Topic 6 33

35 Daily Spiral Review Bill and Ron each ate part of a candy bar. The models below are shaded to show the part that each boy had left. Which of the following compares the portions of candy bars that were left? A B C D The first clock below shows when Shane arrived at the library. The second clock shows when he left. How much time did Shane spend at the library? A.M. to P.M. 3. Order the following numbers from greatest to least: 180, 108, 118, , 180, 118, Mrs. Bird s class baked 45 cupcakes for the fundraiser. They sold 23 cupcakes. Write the number sentence that tells how many cupcakes were NOT sold Keisha bicycles 18 kilometers each day. If she cycles the same distance each day, how far does she cycle in 7 days? km 6. Raul and Mischa measure the same wall. Raul says it is 60 inches long. Mischa says it is 5 feet long. Explain how they can both be right. 1 foot 12 inches; 5 feet 60 inches Daily Spiral Review 6-4 A 4 hours B 4 hours 30 minutes C 5 hours D 5 hours 30 minutes Topic 6 33

36 Problem of the Day Topic 6 Problem of the Day 6-4 Use the table to decide who came in first. (Hint: Use logical reasoning.) Diane was third. Desi was NOT first. Kevin was second. 1st 2nd 3rd 4th Kevin Diane Whitney Desi Problem of the Day 6-4

37 Quick Check Taryn knits scarves for her Design class. She knits gray, white, and brown scarves. There are 7 scarves in all. There is one more white scarf than gray scarf. There are 2 black scarves. Which number shows how many gray scarves Taryn knit? A 2 B 3 C 4 D 5 2. Karim has 11 toy cars in his collection. He has 5 sports cars. There are twice as many race cars as trucks. Which lists the correct number and type of cars Karim has in his collection? A 5 sports cars, 6 race cars, and 3 trucks B 5 sports cars, 2 race cars, and 4 trucks C 5 sports cars, 4 race cars, and 2 trucks D 5 sports cars, 2 race cars, and 1 truck 3. Writing to Explain Write a number sentence that illustrates and answers the following: The Jaguars scored 35 points in the first half of a basketball game. They scored 3 more points in the fourth quarter than they scored in the third quarter. The opposing team scored 90 points and won. How many points might the Jaguars have scored in the third and fourth quarters? Quick Check 6-4 Topic 6 35

38 Quick Check Taryn knits scarves for her Design class. She knits gray, white, and brown scarves. There are 7 scarves in all. There is one more white scarf than gray scarf. There are 2 black scarves. Which number shows how many gray scarves Taryn knit? A 2 B 3 C 4 D 5 2. Karim has 11 toy cars in his collection. He has 5 sports cars. There are twice as many race cars as trucks. Which lists the correct number and type of cars Karim has in his collection? A 5 sports cars, 6 race cars, and 3 trucks B 5 sports cars, 2 race cars, and 4 trucks C 5 sports cars, 4 race cars, and 2 trucks D 5 sports cars, 2 race cars, and 1 truck 3. Writing to Explain Write a number sentence that illustrates and answers the following: The Jaguars scored 35 points in the first half of a basketball game. They scored 3 more points in the fourth quarter than they scored in the third quarter. The opposing team scored 90 points and won. How many points might the Jaguars have scored in the third and fourth quarters? See student samples to the right. Quick Check 6-4 Topic 6 35

39 Problem Solving: Use Objects and Reasoning Reteaching 6-4 Andrea made a design with the figures shown at the right. She placed all the figures in a row. No figure was next to a figure with the same number of sides as itself. No two shaded figures or unshaded figures were next to each other. The first figure in the design was a trapezoid. How did Andrea arrange the rest of her design? Reteaching 6-4 Understand Plan Solve You know the trapezoid is first. It has 4 sides and is shaded. You need to find the order of the figures in the design. You can use the clues you have to place the figures. Draw a picture to help. Draw four spaces in a row. The next figure cannot have 4 sides or be shaded. The triangle is second. It has 3 sides and is unshaded. The next figure cannot have 3 sides or be unshaded. The pentagon is third. It has 5 sides and is shaded. The next figure cannot have 5 sides or be shaded. The square is fourth. It is the only figure left. It has 4 sides and is unshaded. Look Back Is this the only solution to Andrea s design? 1. Draw a figure that could go after the square in Andrea s design above. Remember to follow the rules of the design. 2. Look at the design on the right. Fill in the next two figures and then write a description of them. a b a. b. 36 Topic 6

40 Problem Solving: Use Objects and Reasoning Reteaching 6-4 Andrea made a design with the figures shown at the right. She placed all the figures in a row. No figure was next to a figure with the same number of sides as itself. No two shaded figures or unshaded figures were next to each other. The first figure in the design was a trapezoid. How did Andrea arrange the rest of her design? Reteaching 6-4 Understand Plan Solve You know the trapezoid is first. It has 4 sides and is shaded. You need to find the order of the figures in the design. You can use the clues you have to place the figures. Draw a picture to help. Draw four spaces in a row. The next figure cannot have 4 sides or be shaded. The triangle is second. It has 3 sides and is unshaded. The next figure cannot have 3 sides or be unshaded. The pentagon is third. It has 5 sides and is shaded. The next figure cannot have 5 sides or be shaded. The square is fourth. It is the only figure left. It has 4 sides and is unshaded. Look Back Is this the only solution to Andrea s design? 1. Draw a figure that could go after the square in Andrea s design above. Remember to follow the rules of the design. 2. Look at the design on the right. Fill in the next two figures and then write a description of them. a b a. b. Check student drawings. Check student descriptions. Check student descriptions. 36 Topic 6

41 Problem Solving: Use Objects and Reasoning 1. Use the numbers 5 through 9 to fill the spaces in the square. Each row and column must have a sum of An, Larissa, Sue, and Jen are sitting in a line in a roller coaster. Larissa is sitting right in front of An. Sue is sitting right behind Jen. Jen is not sitting in the front seat. In what order are the girls sitting? Practice What number am I? My tens digit is 3 more than my thousands digit. My ones digit is 2 times my hundreds digit. My tens digit is 4 times my hundreds digit. My tens digit is 1 more than 7. Practice Jay made a bracelet in art class using beads. He used the four beads on the right. Use the clues to guess what the pattern was. The square bead is next to the triangle. The hexagon is not next to the pentagon. No two beads with an even number of sides are next to each other. The last bead is the pentagon. 5. Mark is making a tile design to cover a rectangle. So far, he has used 2 squares and 2 triangles. How many and what shape tiles could Mark use to finish his design? 6. Draw a picture of Mark s design. Topic 6 37

42 Problem Solving: Use Objects and Reasoning 1. Use the numbers 5 through 9 to fill the spaces in the square. Each row and column must have a sum of An, Larissa, Sue, and Jen are sitting in a line in a roller coaster. Larissa is sitting right in front of An. Sue is sitting right behind Jen. Jen is not sitting in the front seat. In what order are the girls sitting? Larissa, An, Jen, Sue 5, What number am I? My tens digit is 3 more than my thousands digit. My ones digit is 2 times my hundreds digit. My tens digit is 4 times my hundreds digit. My tens digit is 1 more than Jay made a bracelet in art class using beads. He used the four beads on the right. Use the clues to guess what the pattern was. The square bead is next to the triangle. The hexagon is not next to the pentagon. No two beads with an even number of sides are next to each other. The last bead is the pentagon. Practice Practice Mark is making a tile design to cover a rectangle. So far, he has used 2 squares and 2 triangles. How many and what shape tiles could Mark use to finish his design? Sample answer: two triangles 6. Draw a picture of Mark s design. Topic 6 37

43 Building Factors Luisa lives in an apartment building. The building has 3 floors. On each floor lives a family of 5. The 1st floor has a family with 2 parents and 3 children. The 2nd floor has 2 grandparents and 3 children. The 3rd floor has 1 parent, 1 grandmother, and 3 children. Each person in the building has 2 pairs of shoes. 1. How many pairs of shoes are in the building? Enrichment 6-4 Reasoning The adults on all 3 floors each have 3 books from the library. Enrichment How many books from the library are in the building? The children on the 1st floor and the children on the 3rd floor each have 6 compact discs. 3. How many compact discs are in the building? The adults on the 1st floor, the adults on the 2nd floor, and 2 children on the 3rd floor each have 7 pairs of white socks. 4. How many pairs of white socks are in the building? 38 Topic 6

44 Building Factors Luisa lives in an apartment building. The building has 3 floors. On each floor lives a family of 5. The 1st floor has a family with 2 parents and 3 children. The 2nd floor has 2 grandparents and 3 children. The 3rd floor has 1 parent, 1 grandmother, and 3 children. Each person in the building has 2 pairs of shoes. 1. How many pairs of shoes are in the building? pairs of shoes Enrichment 6-4 Reasoning The adults on all 3 floors each have 3 books from the library. Enrichment How many books from the library are in the building? books The children on the 1st floor and the children on the 3rd floor each have 6 compact discs. 3. How many compact discs are in the building? compact discs The adults on the 1st floor, the adults on the 2nd floor, and 2 children on the 3rd floor each have 7 pairs of white socks. 4. How many pairs of white socks are in the building? pairs of white socks 38 Topic 6

45 Mark the best answer. 1. There are 58 songs on Yasmin s play list. If m represents the number of rock songs, which expression represents the number of other songs? (6-1) A 58 m B 58 m C 58 m D 58 m 2. Based on the pattern in the table, how many eggs will Vic s hens lay if he has 7 hens in the hen house? (6-2) Number of Hens (h) Total Eggs A 20 B 24 C 28 D Each book in a series has 9 chapters. Which is a way to find the number of chapters there are if the series has 12 books? (6-3) Books (b) Chapters A Subtract 9 from 12. B Divide 12 by 9. C Multiply 12 by 9. D Add 9 and What is a rule for the table? (6-2) Suit Price (p) After Discount A p 12 B p 12 C p 18 D p 18 Topic 6 Multiple-Choice Test Small Medium Large X-large $112 $130 $148 $166 $94 $112 $130 $148 Topic 6 39 Topic 6 Multiple-Choice Test

46 Mark the best answer. 1. There are 58 songs on Yasmin s play list. If m represents the number of rock songs, which expression represents the number of other songs? (6-1) A 58 m B 58 m C 58 m D 58 m 2. Based on the pattern in the table, how many eggs will Vic s hens lay if he has 7 hens in the hen house? (6-2) Number of Hens (h) Total Eggs A 20 B 24 C 28 D Each book in a series has 9 chapters. Which is a way to find the number of chapters there are if the series has 12 books? (6-3) Books (b) Chapters A Subtract 9 from 12. B Divide 12 by 9. C Multiply 12 by 9. D Add 9 and What is a rule for the table? (6-2) Suit Price (p) After Discount A p 12 B p 12 C p 18 D p 18 Topic 6 Multiple-Choice Test Small Medium Large X-large $112 $130 $148 $166 $94 $112 $130 $148 Topic 6 39 Topic 6 Multiple-Choice Test

47 Give each answer. Complete each table. 1. n n 4 4 Topic 6 Free-Response Test Complete each table. Write a rule. 4. p p b b 3 5. k k f y f y t t Topic 6 Free-Response Test 42 Topic 6

48 Give each answer. Complete each table. Topic 6 Free-Response Test Complete each table. Write a rule. 1. n n 4 4. p p b b Add 5 k k Subtract 3 f y f y Add t t Subtract 9 Topic 6 Free-Response Test 42 Topic 6

49 Topic 6 Performance Assessment The staff at the Mountaintop School is preparing for the new school year. There s a lot to get ready. The staff is using tables to help them in their preparations. 1. The secretary is ordering pencils. Complete the table to find the number of pencils in 8 boxes. Write a rule. Then write the expression. Number of Boxes, n Number of Pencils Mrs. Chad made a table to help her with ordering paper and crayons. Complete the table. Write a rule. Then write the expression. Pads of Paper, x Boxes of Crayons Mr. Pero made a table to show the relationship between the number of books in the classroom and the number of students. Complete the table. Write a rule. Then write the expression. Number of Books, a Number of Students The custodian sets up each classroom with 5 extra chairs. What expression can he use to find the number of chairs needed in a classroom with 28 students? Complete the table. Topic 6 Performance Assessment 44 Topic 6 Number of Students, s Number of Chairs

50 Topic 6 Performance Assessment The staff at the Mountaintop School is preparing for the new school year. There s a lot to get ready. The staff is using tables to help them in their preparations. 1. The secretary is ordering pencils. Complete the table to find the number of pencils in 8 boxes. Write a rule. Then write the expression. Number of Boxes, n Number of Pencils Rule: multiply by 12; Expression: n Mrs. Chad made a table to help her with ordering paper and crayons. Complete the table. Write a rule. Then write the expression. Pads of Paper, x Boxes of Crayons Rule: subtract 8; Expression: x 8 3. Mr. Pero made a table to show the relationship between the number of books in the classroom and the number of students. Complete the table. Write a rule. Then write the expression. Number of Books, a Number of Students Rule: divide by 5; Expression: a 5 4. The custodian sets up each classroom with 5 extra chairs. What expression can he use to find the number of chairs needed in a classroom with 28 students? Complete the table. Topic 6 Performance Assessment 44 Topic 6 Number of Students, s Number of Chairs s

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