? Name 8.4 Essential Question Represent and Solve Multi-Step Problems How can you represent and solve multi-step problems using equations? lgebraic Reasoning 5.4. MTHEMTIL PROESSES 5.1., 5.1. Unlock the Problem Shaniqua buys 140 small beads and 30 large beads to make bracelets. She makes 5 bracelets. She uses 13 beads on each bracelet. How many beads does Shaniqua have left? Underline the important information. Example 1 Use multiple single-step equations. STEP 1 Find the total number of beads Shaniqua buys. 140 + 30 = a total number of small beads total number of large beads _ = a 140 30 a total number of beads Shaniqua buys STEP 2 Find the total number of beads Shaniqua uses to make 5 bracelets. 5 13 = d 13 13 13 13 13 5 bracelets with 13 beads _ = d d total number of beads Shaniqua uses STEP 3 Find the total number of beads Shaniqua has left. 170 65 = s beads left beads used _ = s s 65 170 total number of beads Shaniqua buys So, Shaniqua has _ beads left. Module 8 341
Try This! Sometimes you can use one multi-step equation to solve a problem. Miguel sorts his seashell collection into boxes. He has 3 boxes with 15 periwinkle shells in each box. He has 2 boxes with 7 clamshells in each box. He gives his little brother 10 shells. How many shells does he have now? 15 15 15 7 7 total number of shells 3 15 + 2 7 10 = n _ + _ _ = n 10 n _ _ = n _ = n shells given away shells left Example 2 Meagan has two card-collection books. The first book has 8 cards on each of 14 pages. The second book has 6 cards on each of 15 pages. Which of the two books has more cards? STEP 1 Solve the equation b 8 = 14 to find the number of cards in the first book. 14 14 14 14 14 14 14 14 Write a related multiplication equation. 14 _ = b b = _ b STEP 2 Solve the equation p 6 = 15 to find the number of cards in the second book. STEP 3 ompare the number of cards in each book. 15 15 15 15 15 15 The first book has _ cards. The second book has _ cards. 342 Write a related multiplication equation. 15 _ = p p = _ p Since _ > _, the _ book has more cards. Math Talk Mathematical Processes Explain why you can use a related multiplication to solve a division problem.
Name Share and Show Use equations to solve each multi-step problem. 1. caterer is making 3 trays of 24 sandwiches and 2 trays of 30 sandwiches. She receives an order for 35 sandwiches. How many sandwiches, s, does the caterer have left? 2. baseball league has a total of 156 players. The players are divided into 12 equal teams. Each team has 3 coaches. ll players and coaches receive 2 jerseys. How many jerseys, j, will each team receive? Problem Solving Write Math Show Your Work Use equations to solve. 3. Multi-Step florist makes 4 floral arrangements that are exactly the same. He uses 4 bunches of 8 tulips and 2 bunches of 10 daisies. How many flowers, f, are in each arrangement? 4. Multi-Step Francois is rolling coins. He has 3 rolls of 40 quarters. He has 8 rolls of 50 dimes. He exchanges 2 rolls of dimes for 1 roll of quarters. How many coins, c, does Francois have? 5. Multi-Step Elsa has 4 trays of 15 sedimentary rocks. She has 6 trays of 12 metamorphic rocks. She gives away 5 sedimentary rocks for 7 metamorphic rocks. How many rocks, r, does she have? 6. nalyze Murial alternates her exercise. She runs 5 miles each day for 3 days and walks 4 miles each day for 2 days in one week. She rides her bike 8 miles each day for 4 days the next week. How many more miles, m, does Murial travel during the second week than the first week? Module 8 Lesson 4 343
aily ssessment Task Mathematical Processes Fill in the bubble completely to show your answer. 7. pply volunteer took 3 cups and 7 quarts of a large bowl of soup home from a cooking class.. How much soup did this volunteer take? (Hint: There are 4 cups in a quart.) 31 cups 37 cups 31 quarts 42 quarts 8. What is the first step in solving the equation 4 + 10 3 2 = n? Find 4 + 10. Find 3 2. Find 10 3. Subtract n. 9. Multi-Step Evelyn has 4 boxes with 8 pieces of sidewalk chalk in each box. She has 3 boxes with 9 stickers in each box. She gets 5 more pieces of sidewalk chalk from her brother. If she places everything into a bin, how many items does she place in the bin? 24 55 64 72 TEXS Test Prep 344 10. The cost of 3 pizzas is shared equally by 6 people. Each pizza costs $9. Each person contributes $5. Which equation could be used to find, m, the amount of money left? 3 9 6 5 = m 6 5 3 9 = m 9 3 6 5 = m 3 9 + 5 6 = m
Homework and Practice Name lgebraic Reasoning 5.4. MTHEMTIL PROESSES 5.1., 5.1. 8.4 Represent and Solve Multi-Step Problems Use equations to solve. 1. Last week, Mary picked 4 baskets of 8 tomatoes from her garden. This week, she picked 3 baskets of 13 tomatoes. How many more tomatoes, t, does Mary pick this week than last week? 2. costume designer sews 4 rows of 16 beads on a princess costume, 5 rows of 15 beads on a butterfly costume, and 3 rows of 17 beads on a ballerina costume. How many more beads, b, are sewn on the costume with the most beads than are sewn on the costume with the least number of beads? 3. Venancio needs to paint 8 game boards for the carnival. Each game board is divided into 12 parts. He paints 5 parts of 8 game boards yellow, 3 parts of 6 game boards red, 2 parts of 7 game boards green, and 15 parts purple. How many more parts, p, does Venancio have left to paint? 4. Mr. Gates buys frozen yogurt bars for the grade 5 picnic. He buys 3 packages of 12 strawberry yogurt bars and 6 packages of 8 banana yogurt bars. He gives an equal number of frozen yogurt bars to each of 3 classes. How many frozen yogurt bars, y, does each class get? Problem Solving 5. Rusty has a cap collection. He has 2 shelves with 9 football team caps on each shelf. He has 3 shelves with 11 baseball caps on each shelf. He gives his best friend 2 football caps and 3 baseball caps. How many caps, c, does Rusty have now? 6. Erin pays $3 for each of 4 headbands and $2 for each of 5 barrettes. How much more money, m, does Erin pay for all the headbands than for all the barrettes? Module 8 Lesson 4 345
Lesson heck TEXS Test Prep Fill in the bubble completely to show your answer. 7. Marty is using balloons to decorate for a party. She has 3 groups of 5 pink balloons and 4 groups of 3 yellow balloons. She also has 6 white balloons. Which equation could be used to find, b, the total number of balloons? 3 5 + 4 3 = b 3 + 5 + 4 + 3 + 6 = b 3 5 + 4 3 + 6 = b 3 5 4 3 = b 8. For the bake sale, 6 people each bake two dozen oatmeal cookies. Each person eats 2 cookies and then delivers the remaining cookies to the bake sale. Which equation could be used to find, c, the number of oatmeal cookies at the bake sale? 6 2 12 6 2 = c 6 12 6 2 = c 2 12 6 2 = c 6 2 6 2 = c 9. Jasper used 15 inches of blue ribbon, 14 inches of yellow ribbon, and 3 feet of red ribbon to decorate his box of cookies. How many inches of ribbon did Jasper use? 65 inches 32 inches 93 inches 29 inches 10 William used 10 ounces of plain milk and 4 pints of chocolate milk when making the restaurant milkshake recipe. How many ounces of milk did William use? (Hint: there are 16 ounces in a pint.) 64 ounces 40 ounces 26 ounces 74 ounces 11. Multi-Step Rona has 4 packs of 12 glitter pens. She has 7 packs of 8 scented pens. She gives her friend a pack of glitter pens in exchange for a new pack of scented pens. How many pens does Rona have now? 92 12. Multi-Step ella has potted plants on her patio. She has 4 pots with 3 begonia plants in each pot. She has 3 pots with 8 petunias in each pot. She plants 7 more zinnia plants in another pot. How many plants does ella have on her patio? 25 346 104 100 112 43 36 57
Name oncepts and Skills Module 8 ssessment 1. Which value of n makes the equation, n + 5 = 4 + 4, true? q TEKS 5.4. Use the strip diagram to write an equation. Then solve. q TEKS 5.4 2. Eric jogged 15 laps around a track. Margo jogged 5 laps. How many more laps did Eric jog than Margo? Eric Margo 5 15 x 3. Sadie hit 17 golf balls from her bucket. Then there were 33 golf balls left in the bucket. How many golf balls did Sadie have in her bucket before she hit any golf balls? 33 17 g Equation: x = _ Equation: g = _ Write an equation. Then solve. q TEKS 5.4. 4. store sells 8 small, 18 medium, and 20 large sweatshirts. Each sweatshirt costs $16. How much money, m, is the store paid for all the sweatshirts they sell? 5. caterer makes sandwiches from 8 loaves of bread. Each loaf makes 10 sandwiches. The caterer puts 3 ounces of turkey on each sandwich. How many ounces, z, of turkey does the caterer use? 6. train has 34 passengers in each of 3 cars and 28 passengers in each of 4 cars. How many passengers, p, are on the train? 7. There are 252 students at a school party. They are seated in groups of 9. Each group gets 3 bags of popcorn. How many bags of popcorn, p, are used for the party? Module 8 347
Fill in the bubble completely to show your answer. 8. Ryan has 5 boxes with 8 markers in each box. He has 7 boxes with 10 markers in each box. He gives his friend one box of 8 markers and one box of 10 markers. Which equation can be used to find the total number of markers, m, that Ryan has left? q TEKS 5.4. TEXS Test Prep 7 10 5 8 8 10 = m 8 5 8 + 10 7 10 = m 5 8 7 10 8 10 = m 5 8 + 7 10 8 10 = m 9. Thora had $5 left in her pocket after spending $12 on snacks and souvenirs on a class trip. How much money did Thora take on the class trip? The equation t 12 = 5 can be used to find t, the amount of money Thora took on the class trip. q TEKS 5.4 $17 $7 $14 $16 10. Students earned $368 selling c, calendars. They earned $456 selling m, mugs. The price of each mug and each calendar is $8. The equation c = 368 8 represents the number of calendars they sold. The equation m = 456 8 represents the number of mugs they sold. How many more mugs than calendars did students sell? q TEKS 5.4. 57 103 11 46 11. There are 180 students at summer camp. Each cabin houses 12 students. There are 2 counselors for each cabin. Solve the equation c = (180 12) 2 to find the number of c, counselors. q TEKS 5.4. 348 Record your answer and fill in the bubbles on the grid. e sure to use the correct place value.. 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9