Buying at the Stock-Up Sale

Transcription

1 Buying at the Stock-Up Sale Objective To guide children as they multiply using mental math and the partial-products algorithm. 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 Differentiation Options Key Concepts and Skills Apply place-value concepts to find partial products. [Number and Numeration Goal 1] Use multiplication facts to make estimates and calculate partial products. [Operations and Computation Goal 3] Use the partial-products algorithm to multiply 1-digit by multidigit numbers. [Operations and Computation Goal ] Make reasonable estimates. [Operations and Computation Goal 5] Key Activities Children make up and solve problems about costs of multiple items advertised on the Stock-Up Sale posters. Materials Math Journal 2, p. 217 Student Reference Book, pp. 216 and 217 Home Link 9 Math Masters, pp. 399 and 00 (optional) slate tool-kit coins (optional) Playing Fraction Top-It Student Reference Book, p. 287 Math Masters, p. 398 per partnership: 1 deck of Fraction Cards Children practice comparing fractions. Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip (Math Masters, page 398). [Number and Numeration Goal 6] Math Boxes 9 5 Math Journal 2, p. 218 Children practice and maintain skills through Math Box problems. Home Link 9 5 Math Masters, p. 283 Children practice and maintain skills through Home Link activities. READINESS Estimating Costs Math Masters, p. 28; p. 399 (from Part 1) Student Reference Book, pp. 216 and 217 tool-kit dimes Children estimate the money they need to make purchases at the Stock-Up Sale. ENRICHMENT Solving Multistep Number Stories Student Reference Book, pp. 216 and 217 Math Masters, p. 285 Children estimate and solve multistep number stories. Advance Preparation Copy and cut apart the play money on Math Masters, pages 399 and 00 (optional). Teacher s Reference Manual, Grades 1 3 p Unit 9 Multiplication and Division

2 Getting Started Mental Math and Reflexes Have children practice quick recall of basic multiplication facts. Suggestions: , , ,000 Math Message Turn to page 217 in your Student Reference Book. Estimate whether $10 is enough to buy rolls of gift-wrapping paper. Record your estimate on your slate. Discuss your estimation strategy with a partner. Home Link 9 Follow-Up Briefly review answers. Have volunteers model the partial-products algorithm for some of the problems. 1 Teaching the Lesson Math Message Follow-Up (Student Reference Book, p. 217; Math Masters, pp. 399 and 00) WHOLE-CLASS DISCUSSION Discuss children s answers. Possible estimation strategies: Change $2.35 to a close-but-easier amount, such as $2.50. $2.50 = $10.00 (double $2.50 twice). $10 would be enough to buy rolls if they were $2.50 per roll. Because $2.50 is more than $2.35, the cost of rolls at $2.35 is less than $10. Round $2.35 to the nearest $0.10, which is $2.0. $2.00 = $8.00, and $0.0 = $1.60. Therefore, $2.0 = $9.60. Because $2.0 is more than $2.35, the cost is less than $10. Remind children that many problems can be solved with estimation instead of exact calculation. An efficient estimation strategy requires simple mental math and gives an answer that is reasonably close to the exact answer. Have children work in small groups to find the exact cost, using mental math or an algorithm. $9.0 Take time to have children share strategies. For example: $2.00 = $8.00 $0.30 = $1.20 $0.05 = $0.20 $ $ $0.20 = $9.0 Stock-Up Sale Poster #2 Greeting Cards Box of 12 $3.29 You pay $2.63 per box Toothbrush $1.38 You pay $1.13 per brush Bath Soap $0.88 You pay $0.65 per bar Garbage Bags $3.75 You pay $3.18 per box Gift Wrapping Paper $2.35 per roll Night Light Bulbs 2-Pack $0.96 You pay $1.86 per roll You pay $0.76 per pack Data Bank Adjusting the Activity ELL Glue $1.15 Construction Paper $0.67 per pad Shoelaces $1.27 per pair Provide dollar bills (Math Masters, pages 399 and 00) and tool-kit coins for children to use as they act out the problems. You pay $0.9 per bottle You pay $0.5 per pad You pay $1.08 per pair 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 Student Reference Book, p _28_EMCS_S_G3_SRB_DBA_ indd 217 2/17/11 9:8 AM Lesson

3 Data Bank Stock-Up Sale Poster #1 Light Bulbs -Pack $1.09 Extension Cord $3.25 Tissues $0.73 Applying the Partial-Products Algorithm (Student Reference Book, pp. 216 and 217) PROBLEM SOLVING WHOLE-CLASS You pay $0.88 per pack Transparent Tape $0.8 You pay $0.65 per roll Ballpoint Pen $0.39 You pay $0.27 per pen You pay $2.79 per cord Batteries -Pack $3.59 You pay $2.90 per pack Tennis Balls Can of 3 $2.59 You pay $1.86 per can You pay $0.57 per box Toothpaste $1.39 You pay $1.1 per tube Paperback Book $2.99 You pay $2.25 per book Various items are advertised on the two Stock-Up Sale Posters. You or the children use the given prices to suggest number stories that can be solved in two steps. Prior to solving each number story, have children estimate the answer. Next they represent the number story with a number model and use a letter for the unknown quantity and parentheses to show the first calculation. Then they find the answer using the partial-products algorithm (Lesson 9-) with dollars and cents. For the first few stories, write the problems on the board while the children suggest the number models for the partial products. Student Reference Book, p _28_EMCS_S_G3_SRB_DBA_ indd 216 2/17/11 9:8 AM For example: How much change would you receive if you bought 5 packs of batteries at the stock-up sale price and paid with a $20 bill? (Story examples are based on Student Reference Book, pages 216 and 217.) NOTE Explain to children that stores often encourage customers to spend more by reducing the price of an item purchased in bulk. Stores make up for the lower profit per item by selling more items. NOTE Some children might use mental arithmetic to find the exact answer, thinking of the solution as: 5 $0.10 = $0.50; $15 $0.50 = $1.50; $20 $1.50 = $5.50. Praise this strategy; however, since the focus of this lesson is on the partialproducts algorithm, make sure to emphasize the strategy described in this activity. Remind children of the Guide to Solving Number Stories on Math Masters, page 06. What do you want to find out? The amount of change you would receive from $20 What do you know from reading the story and looking at the Stock-Up Sale Poster? 5 packs of batteries are purchased and each pack costs the sale price of $2.90. Ask partners to work together to estimate the answer. After a few minutes, discuss children s answers. One possible estimation strategy is to round $2.90 to the nearest dollar, which is $3.00. $ is $ The difference between $20.00 and $15.00 is $5, so the answer to the number story should be about $5. Explain that because the number story asks for the amount of change, we need to calculate to find the exact answer. Ask: Will the exact answer be more or less than $5? More, because we rounded the price of one pack of batteries up to $3. What is a first step to solve the problem? Find the cost of 5 packs of batteries. How might you do this? Multiply $ Write $ on the board. What symbols can we use in the number model to show that this is the first step? Add parentheses around $ What is the second step? Subtract that product from $ How can we write this step? Indicate the first step using parentheses, then subtract from $20. Write the step on the board: $20 ($2.90 5). Since we want to find the amount of change, use C for the unknown quantity in the open sentence: $20 ($2.90 5) = C. 738 Unit 9 Multiplication and Division

4 Links to the Future At this time, children are not expected to know the conventional order of operations, so parentheses tell them which operation comes first. Understanding that grouping symbols can be used to affect the order in which operations are carried out is a Grade 3 Grade-Level Goal. Describing and applying the conventional order of operations is a Grade 6 Grade-Level Goal. Take a few minutes to reconnect each expression in the number model with the problem situation. What is $20? The amount of money used to pay for the batteries What is $2.90? The cost of 1 pack of batteries Why are we multiplying $2.90 by 5? To find the cost of 5 packs of batteries Because the calculation in parentheses is solved first, write the multiplication problem on the board. Ask children to suggest number models for the partial products. $ [$2.00s] [$0.90s] +.50 $1.50 Ask: Is $1.50 the answer to the number story? no Why? $1.50 tells how much 5 packs of batteries cost, but we still need to find out how much change is left from $20. What is the second step? Subtract $1.50 from $20. Have children complete the calculation: $20 $1.50 = $5.50. What is the answer to the number story? You would get $5.50 change. Does your answer make sense? yes Date 9 5 Time Shopping at the Stock-Up Sale Use the Stock-Up Sale Posters on pages 216 and 217 in the Student Reference Book. Solve each number story below. There is no sales tax. For each problem: Estimate the answer. Write a number model with parentheses to show which step is first. Use a letter to show what you want to find out. Solve for the exact answer. Show your work. 1. Jeff bought 5 toothbrushes and 1 tube of toothpaste. What is the total cost? Estimate: The total cost is about $7.0. (5 $1.13) + $1.39 = T Answer: $7.0 Does your answer make sense? Explain. Yes, my estimate was about $7.0 and my answer was $7.0. They are close. 2. Mr. De la Garza pays for 8 boxes of tissues with a $5.00 bill. How much change will he get? Estimate: He will get about $0.20. $5.00 (8 $0.57) = C Answer: $0. workspace Does your answer make sense? Explain. Sample answers: Yes, because the amount of change is less than what he started with; my answer is close to my estimate. Math Journal 2, p _EMCS_S_MJ2_G3_U09_57618.indd 217 3/11/11 1:5 PM How do you know? Sample answers: Before I solved for the exact answer, I estimated the change to be about $5. $5.50 is close to $5; I know my answer has to be less than $20 because some of the money was spent on batteries. Does your answer make the number model true? yes Write a summary number model on the board: $20 ($2.90 5) = $5.50. Pose another number story: How much would it cost to buy 5 pads of construction paper and 1 bottle of glue? What do you want to find out? The total cost of the construction paper and 1 bottle of glue What do you know from reading the story and looking at the poster? I know that if you buy 5 or more pads you get the stockup sale price. One pad of construction paper at the sale price is $0.5 and 1 bottle of glue at the regular price costs $1.15. A possible number model for the story is ($0.5 5) + $1.15 = T. What is the answer? The total cost is $3.85. As needed, continue to suggest number stories involving two or more steps to solve with the class. Fraction Top-It Materials 1 deck of Fraction Cards (Math Journal 2, Activity Sheets 5 8) Players 2 Skill Comparing fractions Object of the game To collect more cards. Directions 1. Shuffle the Fraction Cards and place the deck picture-side down on the table. 2. Each player turns over a card from the top of the deck. Players compare the shaded parts of the cards. The player with the larger fraction shaded takes both cards. 3. If the shaded parts are equal, the fractions are equivalent. Each player then turns over another card. The player with the larger fraction shaded takes all the cards from both plays.. The game is over when all cards have been taken from the deck. The player with more cards wins. Players turn over a 3_ card and a _ 6 card. The 3_ card has a larger shaded area. The player holding the 3_ card takes both cards. Players turn over a 1_ 2 card and a _ 8 card. The shaded parts are equal. Each player turns over another card. The player with the larger Fraction Card takes all the cards. Student Reference Book, p Games 8 267_31_EMCS_S_G3_SRB_GAM_ indd 287 2/17/11 10:0 AM Lesson

5 Date 9 5 Math Boxes 1. Fill in the oval for the best answer. The perimeter of the quadrangle is 21 yd. 30 yd. 6 yd 15 yd 2 yd. 2 yd. 3. Use the partial-products algorithm to solve Time 2. Draw a -by-9 array of Xs. How many Xs in all? 36 Write a number model.. Solve. 9 = (0 3) 2 = 60 (300 6) = 200 (7 80) + 10 = Draw a set of 12 circles. Color 5_ 12 of the set blue. Color 1_ 3 of the set red. Color 1_ 6 of the set green. B B B R R G B B R R G 6. Solve. 1 gram = 1,000 milligrams 2 grams = 2,000 milligrams 5 grams = 5,000 milligrams 1 kilogram = 1,000 grams kilograms =,000 grams Solving Stock-Up Sale Stories (Math Journal 2, p. 217; Student Reference Book, pp. 216 and 217) PARTNER Children work together in partnerships to solve 2-step problems on journal page 217 using the information on pages 216 and 217 in the Student Reference Book. Children write the number models using a letter variable for the unknown quantity. 2 Ongoing Learning & Practice Playing Fraction Top-It (Student Reference Book, p. 287; Math Masters, p. 398) PROBLEM SOLVING PARTNER Math Journal 2, p _EMCS_S_MJ2_G3_U09_57618.indd 218 3/11/11 1:5 PM Children practice comparing fractions by playing Fraction Top-It. For game instructions, see Lesson 8-6 or page 287 in the Student Reference Book. Have children use an Exit Slip to record at least five rounds using the symbols >, <, and = to compare the fraction pairs. Ongoing Assessment: Recognizing Student Achievement Exit Slip Name Date Time HOME LINK 9 5 Family Note Saving at the Stock-Up Sale Today the class used mental math and the partial-products algorithm to solve problems. For each problem below, have your child estimate the answer and then write a number model to represent the story, using a letter for the unknown quantity and parentheses to show which calculation they do first. Note that any letter can be used to represent the unknown quantity Please return this Home Link to school tomorrow. 192 For each problem, make an estimate and then solve for the exact answer. Write a number model using a letter for what you want to find out and use parentheses to show which calculation you do first. 1. Phil has $6.00. He wants to buy Creepy Creature erasers that cost $1.05 each. If he buys 5 or more, they are $0.79 each. Does he have enough money to buy 7 erasers? yes Explain your estimate. If Phil buys 7 erasers, each costs $0.79. $0.79 is close to $0.80 and $ is $5.60. That is less than $6. How much money will Phil have left if he buys 7 Creepy Creature erasers? $ ($0.79 7) = M Answer: Phil has $ 0.7 left. 2. Mrs. Katz is buying apples and carrot cake for a school party. The apples cost $2.12 per pound. The carrot cake costs $ Estimate the cost for 3 pounds of apples and 1 cake. Home Link Master Estimate: About $ Explain your estimate. $2.12 is close to $2 so 3 pounds of apples cost about $6. $19.75 is close to $20. So the total cost is about $26. What is the exact cost for 3 pounds of apples and 1 cake? ($2.12 3) + $19.75 = E Answer: The exact cost is $ Math Masters, p Use an Exit Slip (Math Masters, page 398) to assess children s progress toward comparing fractions. Children are making adequate progress if they are able to record at least 5 pairs of fractions with the appropriate comparison symbols. Some children may be able to compare the fractions without using Fraction Cards. [Number and Numeration Goal 6] Math Boxes 9 5 (Math Journal 2, p. 218) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 9-7. The skill in Problem 6 previews Unit 10 content. Home Link 9 5 (Math Masters, p. 283) INDEPENDENT PROBLEM SOLVING Home Connection Children use mental math or the partial-products algorithm to solve multiplication number stories _EMCS_B_MM_G3_U09_ indd 283 3/10/11 2:2 PM 70 Unit 9 Multiplication and Division

6 3 Differentiation Options READINESS Estimating Costs (Math Masters, p. 28; Student Reference Book, pp. 216 and 217) To provide experience with estimating money amounts, have children determine the number of dollar bills and dimes they need to make purchases. Use the Stock-Up Sale posters on pages 216 and 217 in the Student Reference Book. Children record their work on Math Masters, page 28. ENRICHMENT Solving Multistep Number Stories (Student Reference Book, pp. 216 and 217; Math Masters, p. 285) PARTNER 5 15 Min PARTNER Min Name Date Time 9 5 Dollars and Dimes 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. Items to Be Purchased Example: 1 box of 12 Greeting Cards Price: $ roll of Gift-Wrapping Paper Price: $ roll of Transparent Tape Price: $0.8 1 box of Tissues Price: $ Paperback Book Price: $2.99 Math Masters, p _EMCS_B_MM_G3_U09_ indd 28 Teaching Master Dollars and Dimes Needed 3 dollars 3 dimes Total: $ 3.30 Total: $ Total: $ Total: $ Total: $ dollars dimes dollars dimes dollars dimes dollars dimes /18/11 7:37 PM To provide children with experience with multistep number stories, have them use information from the Stock-Up Sale Posters on Student Reference Book, pages 216 and 217 to solve stories on Math Masters, page 285. For each story, have children estimate and then solve. Explain that when writing number models for number stories with more than two steps, more than one set of parentheses is sometimes needed. For example, consider the following story: Compare the cost of buying paperback books to the cost of buying 5 paperback books. A possible number model could be ($2.99 ) ($2.25 5) = D. The calculations for the costs of books at the regular price and 5 books at the sale price must be done before subtracting to find the difference. NOTE It is also acceptable for children to write a series of number models for number stories with more than two steps. Algorithm Project The focus of this lesson is to apply the partial-products algorithm to money amounts. For enrichment, see Algorithm Project on page A15 to teach U.S. traditional multiplication of decimals using money. Name Date Time 9 5 Solving Multistep Number Stories Use the Stock-Up Sale Posters on pages 216 and 217 in the Student Reference Book. For each problem below, make an estimate and then solve the number story. There is no sales tax. 1. How much more do 5 boxes of garbage bags cost than 3 boxes of garbage bags? Estimate: About $ 3 Explain your estimate. If I buy 5 boxes, I pay $3.18 for each box; if I buy 3 boxes, I pay $3.75 for each box. $3.18 is close to $3 and $3.75 is close to $. $3 5 = $15 and $ 3 = $12. The difference is about $3. (5 $3.18) (3 $3.75) = D Solve. Show your work on the back of the page. Answer: 5 boxes cost $.65 more than 3 boxes. 2. How much more does it cost to buy 5 rolls of wrapping paper than 2 rolls of wrapping paper? Estimate: About $ 2.50 Explain your estimate. If I buy 5 rolls, each roll costs $1.86. If I buy 3 rolls, each roll costs $2.35. I know that $1.86 is close to $2 and $2.35 is close to $2.50, so $2 5 = $10 and $ = $7.50. The difference will be about $2.50. (5 $1.86) (3 $2.35) = D Teaching Master Solve. Show your work on the back of the page. Answer: 5 rolls cost $ 2.25 more than 3 rolls. Math Masters, p _EMCS_B_MM_G3_U09_ indd 285 3/10/11 2:2 PM Lesson

7 Name Date Time HOME LINK 9 5 Saving at the Stock-Up Sale Family Note Today the class used mental math and the partial-products algorithm to solve problems. For each problem below, have your child estimate the answer and then write a number model to represent the story, using a letter for the unknown quantity and parentheses to show which calculation they do first. Note that any letter can be used to represent the unknown quantity. Please return this Home Link to school tomorrow For each problem, make an estimate and then solve for the exact answer. Write a number model using a letter for what you want to find out and use parentheses to show which calculation you do first. 1. Phil has $6.00. He wants to buy Creepy Creature erasers that cost $1.05 each. If he buys 5 or more, they are $0.79 each. Does he have enough money to buy 7 erasers? Explain your estimate. How much money will Phil have left if he buys 7 Creepy Creature erasers? $ ($0.79 7) = M Answer: Phil has $ left. Copyright Wright Group/McGraw-Hill 2. Mrs. Katz is buying apples and carrot cake for a school party. The apples cost $2.12 per pound. The carrot cake costs $ Estimate the cost for 3 pounds of apples and 1 cake. Estimate: About $ Explain your estimate. What is the exact cost for 3 pounds of apples and 1 cake? Answer: The exact cost is $. 283

8 Name Date Time 9 5 Solving Multistep Number Stories Use the Stock-Up Sale Posters on pages 216 and 217 in the Student Reference Book. For each problem below, make an estimate and then solve the number story. There is no sales tax. 1. How much more do 5 boxes of garbage bags cost than 3 boxes of garbage bags? Estimate: About $ Explain your estimate. Solve. Show your work on the back of the page. Answer: 5 boxes cost $ more than 3 boxes. 2. How much more does it cost to buy 5 rolls of wrapping paper than 2 rolls of wrapping paper? Estimate: About $ Explain your estimate. Copyright Wright Group/McGraw-Hill Solve. Show your work on the back of the page. Answer: 5 rolls cost $ more than 3 rolls. 285