Use Strategies and Properties to Multiply by 2-Digit Numbers

Transcription

1 Name Use Strategies and Properties to Multiply by 2-Digit Numbers Home-School Connection Topic 4 Dear Family, Your child is learning how to multiply 2-digit numbers by 2-digit numbers. Some of the strategies he or she is learning to use include arrays and algorithms. Below are examples for Use an array. Add each part of the array to find the product = = = = Use an algorithm. Multiply the ones, then the tens. Add the partial products Multiply the ones Multiply the tens Add the partial products. Multiplying Game Materials number cube (labeled 1 6) Play in pairs. Each player rolls the number cube. Record the number the first player rolls in the tens place and the number the second player rolls in the ones place to create a 2-digit number. Each player rolls the number cube again, recording the numbers in the same way. Then players complete the multiplication. When a player has found the answer, he or she says Done. The other player checks the answer. If it is correct, he or she receives a point. The first player to earn 3 points wins the game. Observe Your Child If your child gets an incorrect answer, help him or her find the error in his or her computation.

2 Nombre Usar estrategias y propiedades para multiplicar por números de 2 dígitos De la escuela al hogar (en español) Tema 4 Estimada familia: Su niño(a) está aprendiendo a multiplicar números de 2 dígitos por números de 2 dígitos. Algunas estrategias que él o ella está aprendiendo incluyen matrices y algoritmos. Debajo hay ejemplos para Usar una matriz. Sumar cada parte de la matriz para hallar el producto = = = = Usar un algoritmo. Multiplicar las unidades y, luego, las decenas. Sumar los productos parciales Multiplicar las unidades Multiplicar las decenas Sumar los productos parciales. Jugar a multiplicar Materiales cubo numérico (rotulado 1 a 6) Jueguen en parejas. Cada jugador lanza el cubo numérico. Anoten el número que obtuvo el primer jugador en la posición de las decenas y el número que obtuvo el segundo jugador en la posición de las unidades para crear un número de 2 dígitos. Cada jugador lanza el cubo numérico otra vez y anota los números de la misma manera. Luego, los jugadores resuelven la multiplicación. Cuando un jugador halla la respuesta, él o ella dice Listo. El otro jugador comprueba la respuesta. Si es correcta, él o ella recibe un punto. El primer jugador en acumular 3 puntos gana el juego. Observe a su niño(a) Si su niño(a) obtiene una respuesta incorrecta, ayúdelo(a) a hallar el error en su cálculo.

3 Name Vocabulary 1. A product is an answer to a multiplication problem. Reteach to Build Understanding 4-1 Find each product. 3 8 = 7 6 = 2 5 = 2. Factors are the numbers that are multiplied together to give a product. Find each missing factor. 9 = 54 4 = 12 6 = 30 Each of the multiplication sentences above is an example of a basic fact. You can use basic facts and patterns to multiply multiples of 10. Look for a pattern in the number of zeros in the factors and the products = 18 Basic fact = 1,800 1 zero + zero = 2 zeros inserted after the product of the basic fact = 20 Basic fact = 2,000 zero + zero = zeros inserted after the product of the basic fact. Use a basic fact and a pattern to multiply = = = = 80 9 = = On the Back! 7. Use basic facts and patterns to find R 4 1

4 Clip and Cover Partner Talk Share your thinking while you work. Get Started or At Your Turn How to Play How to Win Get 10 squares in one color and 10 in another color, two paper clips, and two number cubes. Take turns. Toss two cubes to find your ovals. EXAMPLE: Choose the 3rd oval on the left and the 5th oval on the right, or choose the 5th oval on the left and the 3rd oval on the right. Mark your ovals with paper clips. The number in each oval is a factor. Explain how to use mental math to multiply the numbers. Say a multiplication sentence that includes the product. Find and cover the product. Lose your turn if the answer is taken. The first player or team to get any three connected rectangles in a row or column wins ,200 4,500 1,000 5,400 2,700 1,600 1,200 4, ,200 7,200 2,400 2,100 3,500 2,000 5, If you have more time Explain why some products in the game board have more than two zeros. Play again! Center Game 4 1

5 Clip and Cover Partner Talk Share your thinking while you work. Get Started or At Your Turn How to Play How to Win Get 10 squares in one color and 10 in another color, one paper clip, and one number cube. Take turns. Toss one cube to find your oval. EXAMPLE: Choose the 3rd oval on the left, or choose the 3rd oval on the right. Mark your oval with a paper clip. The number in the oval you chose is a product. Use mental math to find two factors that you can multiply to get the product you chose. Say the multiplication sentence that includes the product you chose. Cover the two factors. Lose your turn if the answer is taken. The first player or team to get any three connected rectangles in a row or column wins. 1,200 6, ,800 4,500 4, ,400 5, ,000 3,600 4, ,800 4,200 If you have more time Play again! Talk about your strategies as you play. Center Game 4 1

6 Name Vocabulary 1. An array is a model used to display objects in rows and columns. This place-value block array models 10 groups of 14. There are groups of 10. There are groups of 4. Reteach to Build Understanding Partial products are products found by breaking one factor into ones, tens, hundreds, and so on and then multiplying each of these by the other factor. Find the product of groups of 10 or = groups of 4 or 10 4 = 40 Add the partial products. + Use the array at the right to find the product of There are groups of 10. There are groups of. Find the partial products = 20 = Add the partial products. + = So, =. 4. Draw an array to find the product of groups of 20 = 30 groups of 6 = + = So, =. On the Back! 5. Draw an array to find the product of R 4 2

7 Teamwork Partner Talk Share your thinking while you work. Get Started or Repeat for Each Round Put in a bag. Pick a tile. Pick two tiles if your group has only two students. Your tile number tells you which job to do. Get paper and a pencil Take turns. On your turn, put in the bag. Pick two tiles. Place the lesser number in the left tile space. Place the greater in the right tile space. Say the 2-digit number that your team will multiply by Do These Jobs in Order 1 Sketch a model of a place-value block array that represents the multiplication Explain how to find the partial product for the right side of the area model. Explain how to find the partial product for the left side of the area model. Explain how to find the product of the two numbers. If you have more time Put back in the bag. Pick tiles to find your jobs for the next round. Replace 20 with a different multiple of ten to use as one factor. Center Game 4 2

8 Teamwork Partner Talk Share your thinking while you work. Get Started Put in a bag. Get 6 colored squares. Repeat for Each Round Get paper and a pencil. Form two teams of two. One team chooses row A and the other team chooses row B at the bottom of the page. Pick a tile. Find the area model next to that tile number. One team explains how to find the partial product for the left section of the model. The other team explains how to find the partial product for the right section of the model. Both teams find the product of the 2-digit numbers. Compare results. The team that chose the row with the answer uses a colored square to cover the product. The first team to cover all three answers wins the game A 2,010 2,900 2,640 B 1, ,240 If you have more time Play the game again! Center Game 4 2

9 Name Vocabulary Reteach to Build Understanding An estimate tells about how many or about how much. It is an approximate value rather than an exact answer = Estimate: 3 10 = 2. Rounding is a process that determines which multiple, of 10, 100, 1,000, and so on, a number is closest to. 43 is closer to than to. 43 rounds to Estimate the product of Round 18 to the nearest ten. 18 is closer to than to 10. Round 34 to the nearest ten. 34 is closer to than to rounds to =. So, is about. 4. Estimate the product of Round 73 to the nearest ten. 73 is closer to than to. Round 47 to the nearest ten. 47 is closer to than to rounds to =. So, is about rounds to. So, is about. On the Back! 6. Use rounding to estimate the product of R 4 3

10 Name Vocabulary 1. Compatible numbers are numbers that are easy to compute mentally. You can use compatible numbers to estimate. Use compatible numbers to estimate is close to 25, and 31 is close to 30. So, is about Remember to look for multiplication patterns =, so = is about. 2. Use compatible numbers to estimate Find compatible numbers. 27 is close to. 42 is close to 40. Use number patterns to multiply the compatible numbers. 4 = 40 = is about. 3. Use compatible numbers to estimate is close to. 68 is close to is about = is about = is about =. On the Back! 6. Use compatible numbers to estimate Reteach to Build Understanding 4-4 R 4 4

11 Think Together Partner Talk Share your thinking while you work. Get Started or Put in a bag. For Each Round Choose A, B, C, D, E, or F. Ask someone to read the directions. Pick a tile. Pick two tiles if your group has only two students. Estimate the product next to your number. Discuss: Which three expressions have the same estimate? Why? Decide: Which expression has a different estimate? Why? AExplain how to estimate each product using compatible numbers B Explain 1 how to estimate each product using compatible numbers CExplain how to estimate each product using compatible numbers DExplain how to estimate each product using compatible numbers E Explain 1 how to estimate each product using compatible numbers F Explain 1 how to estimate each product using compatible numbers If you have more time Make up a Think Together question for this lesson. Challenge your classmates to think together to answer your question. Center Game 4 4

12 Think Together Partner Talk Share your thinking while you work. Get Started or Put in a bag. For Each Round Choose A, B, or C. Pick a tile. Pick two tiles if your group has only two students. Follow the directions next to your number. Do the steps in order. Discuss: How did the group members estimate to answer your question? Decide: Does every group member have a reasonable estimate? Number of A Minutes Spent Doing Chores Each Day Jill 55 Caren 45 Larry 25 Eric 75 B Number of Minutes Writing in a Journal in One Week Howard 75 Quinn 83 Anne 69 Reece 95 C Number of Minutes Practicing Piano Each Day Bill 45 Tim 88 Geena 85 Dona Do These Steps in Order Write a question. To answer your question, group members should estimate a product. Write a second question. To answer your question, group members should estimate a different product. Write a third question. To answer your question, group members should estimate a different product. Write a fourth question. To answer your question, group members should estimate a different product. If you have more time About how many minutes do you spend doing chores in 99 days? Center Game 4 4

13 Name Vocabulary 1. An array is a model used to display objects in rows and columns. You can use an array to find the product of two 2-digit numbers. The array at the right represents Draw lines through the array to show the tens and ones in each factor Reteach to Build Understanding Use the array for to find each partial product = 10 8 = 4 10 = 4 8 = Add the partial products to find the product of = So, =. 3. What two factors are shown by the array at the right?? Draw lines through the array to show the tens and ones in each factor.? Find each partial product, and then add to find the product. = 4. Draw an array to find the product of = On the Back! 5. Draw an array to find the product of R 4 5

14 Name Planning a Wind Farm Math and Science Activity 4-5 Did You Know? A large wind turbine can produce more than one megawatt of electricity. 1 megawatt is the same as 1,000,000 watts. This is enough electricity to light ten thousand 100-watt light bulbs. A wind farm has many wind turbines often arranged in arrays. Some wind farms produce enough electricity for thousands of households. A city of about 200,000 people is planning to build a wind farm. They want the wind farm to generate enough electricity for the entire city. The city estimates that they need at least 6,750 megawatts per hour of electricity. Use the information in the table to decide which plan the city should choose. Megawatts Plan Wind Farm Array per Turbine per Hour A 43 rows of 20 8 B 19 rows of 50 7 C 28 rows of 40 6 D 33 rows of 30 7 Total Number of Turbines Total Megawatts per Hour ➊ Complete the table. ➋ Extension Which plan should the city choose? Explain. Math and Science Activity 4 5

15 Name Vocabulary 1. The Distributive Property states that multiplying a sum by a number is the same as multiplying each number in the sum by that number and adding the products. Reteach to Build Understanding 4-6 Rewrite using the Distributive Property = (30 + 6) (10 + 5) = (30 + 6) 10 + (30 + 6) 5 = (30 ) + (6 ) + (30 ) + (6 ) 2. Use the area model and the Distributive Property to find Break apart 24 and = ( + 4) ( + 9) Multiply (20 + 4) by 10. Multiply (20 + 4) by 9. = (20 + 4) + (20 + 4) Distribute both the 10 and the 9. = (20 ) + (4 ) + (20 ) + (4 ) = = 3. Draw an area model and use the Distributive Property to find = 4. Use the Distributive Property to find = On the Back! 5. Draw an area model and use the Distributive Property to find R 4 6

16 Toss and Talk Partner Talk Share your thinking while you work. Get Started or At Your Turn Get 10 squares in one color and 10 in another color. Get two number cubes. Take turns with another player or team. Toss two number cubes. Add the dots. Find your toss below. Follow the directions. Explain your thinking. Cover the answer. If the answer is taken, lose your turn. Have fun! Toss Match the expression to a way to break apart the factors or a way to use the Distributive Property (40 10) + (40 6) + (3 10) + (3 6) (70 40) + (70 2) + (5 40) + (5 2) (20 20) + (20 4) + (5 20) + (5 4) (40 20) + (40 5) + (2 20) + (2 5) (50 60) + (50 7) + (4 60) + (4 7) (40 50) + (40 3) + (6 50) + (6 3) (30 20) + (30 9) + (7 20) + (7 9) (90 30) + (90 2) + (6 30) + (6 2) (90 30) + (90 2) + (6 30) + (6 2) (90 80) + (90 1) + (1 80) + (1 1) (70 40) + (70 2) + (5 40) + (5 2) (40 10) + (40 6) + (3 10) + (3 6) (10 10) + (10 8) + (9 10) + (9 8) (20 80) + (20 6) + (2 80) + (2 6) (90 80) + (90 1) + (1 80) + (1 1) (40 50) + (40 3) + (6 50) + (6 3) How to Win You win if you are the first to get four connected rectangles, like: Center Game 4 6 If you have more time Play again!

17 Toss and Talk Partner Talk Share your thinking while you work. Get Started or At Your Turn Get 10 squares in one color and 10 in another color. Get two number cubes. Take turns with another player or team. Talk about math as you play! Toss two number cubes. Add the dots. Find your toss below. Follow the directions. Explain your thinking. Cover the answer. If the answer is taken, lose your turn. Have fun! Toss Read what is given. Find an expression that is equivalent to the given expression. Explain your choice. 2 (40 + 6) (50 + 9) 3 (20 + 3) 20 + (20 + 3) 4 7 (30 20) + (6 20) + (30 1) + (6 1) 8 (50 + 8) (30 + 2) 9 (10 + 8) 50 + (10 + 8) 1 4 (80 40) + (1 40) + (80 9) + (1 9) 10 (30 90) + (2 90) + (30 4) + (2 4) 5 (60 + 3) (40 + 7) 11 (50 + 8) (30 + 5) 6 (20 + 4) 40 + (20 + 4) 5 12 (80 30) + (4 30) + (80 3) + (4 3) How to Win You win if you are the first to get four connected rectangles, like: Center Game 4 6 If you have more time Play again!

18 Name Reteach to Build Understanding 4-7 Vocabulary 1. Partial products are products found by multiplying each place value of both factors. 10 = 10 = This area model shows. Each area represents a different partial product. Complete each equation. What are the partial products? 4 = 4 = 2. The area model shows What are the partial products? Multiply the ones. Then, multiply the tens What is 5 2? What is 5 20? What is 10 2? What is 10 20? Add the partial products. What is 2? What is 4? What is? What is? Add the partial products. On the Back! 5. Draw an area model for Use your area model to find the partial products and solve. 5 R 4 7

19 Teamwork Partner Talk Share your thinking while you work. Get Started or Get paper and a pencil. Put in a bag. Repeat for Each Round Choose a, b, c, d, e, or f. Pick two tiles. Display a two-digit number in the empty squares. Take turns as you do the steps listed below in order. Find the number of toys in all. Put the tiles back in the bag. STEP 1 Explain how to find the first two partial products. STEP 2 Explain how to find the second two partial products. STEP 3 Explain how to find the product. STEP 4 Estimate to check that the number of toys in all is reasonable. a b Boxes of toy dogs with 12 dogs in each box Boxes of toy cats with 24 cats in each box c Boxes of toy dinosaurs with 36 dinosaurs in each box d Boxes of toy cars with 48 cars in each box e f Boxes of toy trains with 72 trains in each box Boxes of toy boats with 96 boats in each box If you have more time Repeat the activity. Center Game 4 7

20 Teamwork Partner Talk Share your thinking while you work. Get Started or Repeat for Each Round Get 10 squares in one color and 10 in another color. Get paper and a pencil. Put in a bag. Take turns Pick 4 tiles. Display two 2-digit numbers. Every student multiplies and finds the product. The student or team that chose the tiles covers the digit in the tens place in the product if it is available on the game board. Put the tiles back in the bag. Repeat. x Cover the Digit To win, be the first player or team to cover three digits in the same row. If you have more time Play again. This time, cover the digit in the hundreds place in the product. Center Game 4 7

21 Name Vocabulary Reteach to Build Understanding A multiple is the product of a given whole number and any non-zero whole number. Multiples of 10 are the numbers you say when you count by 10s. Multiples of 10: 10 1 = 10 6 = 10 2 = 10 7 = 10 3 = 10 8 = 10 4 = 10 9 = 10 5 = = 2. Label the grid to model Break apart 18 into tens and ones. 18 = + Find the partial products for = 30 = Add the partial products. + = 3. Now find using an algorithm. Complete the multiplication at the right. Think of 30 as 3 tens. When multiplying by tens, record a 0 in the ones place of the product. Then, multiply by the 3, using an algorithm Multiply to find the product. Draw models as needed = = = On the Back! 7. Find R 4 8

22 Clip and Cover Partner Talk Share your thinking while you work. Get Started or At Your Turn How to Play How to Win Get 10 squares in one color and 10 in another color, two paper clips, paper and a pencil, and two number cubes. Take turns. Toss two cubes to find your ovals. EXAMPLE: Choose the 3rd oval on the left and the 5th oval on the right, or choose the 5th oval on the left and the 3rd oval on the right. Mark your ovals with paper clips. Explain how to multiply the numbers you chose. Use mental math or paper and a pencil. Find and cover the product. Lose your turn if the answer is taken. The first player or team to get any three connected rectangles in a row or column wins ,480 2,520 1,680 5, ,800 1,260 2,100 1, ,170 1,950 2,240 4, ,360 2,610 1,560 2, If you have more time Play again! Talk about the steps you use to find the product. Center Game 4 8

23 Clip and Cover Partner Talk Share your thinking while you work. Get Started or At Your Turn How to Play How to Win Get 10 squares in one color and 10 in another color, one paper clip, paper and a pencil, and one number cube. Take turns. Toss one cube to find your oval. EXAMPLE: Choose the 3rd oval on the left, or choose the 3rd oval on the right. Mark your oval with a paper clip. Explain how to multiply the factors you chose. Find two other factors that have the same product. Use mental math or paper and a pencil. Cover those factors. Lose your turn if the answer is taken. The first player or team to get any three connected rectangles in a row or column wins If you have more time Play again! Talk about your strategies as you play. Center Game 4 8

24 Name Vocabulary 1. An algorithm is a set of steps used to solve a math problem. To find 24 6, you can use an algorithm Multiply the ones. Regroup if necessary. Multiply the tens. Add any extra tens. Reteach to Build Understanding Find Use an algorithm. Step 1 Multiply by the ones. Regroup Step 2 Multiply by the tens. Regroup Step 3 Add the partial products Use an algorithm to find the product = = On the Back! 5. Find Show your work. 2 8 ones = 16 ones Regroup 16 ones as 1 ten, 6 ones. 2 1 ten = 2 tens 2 tens + 1 ten = 3 tens 30 8 ones = 240 ones or 24 tens Regroup 24 tens as 2 hundreds, 4 tens ten = 30 tens or 3 hundreds 3 hundreds + 2 hundreds = 5 hundreds R 4 9

25 Name Vocabulary Reteach to Build Understanding An estimate is an approximate number. Rounding is one way to estimate a product. Estimation can help determine if an answer is reasonable. Use rounding to estimate = Use an algorithm to find the product. 2. Multiply 7 ones by 23. Multiply 6 tens by 23. Add the partial products Use estimation to check if the answer is reasonable. 23 rounds to. 67 rounds to = is close to. The answer is , Use an algorithm to find each product. Use estimation to check if your answer is reasonable = = = = On the Back! 7. Use an algorithm to find Use estimation to check if your answer is reasonable. R 4 10

26 Name Fossil Fuels Math and Science Activity 4-10 Did You Know? Coal, petroleum (oil), and natural gas are fossil fuels. These fuel sources are formed when buried dead plants and animals decompose. This takes thousands and thousands of years. Because this process takes so long, these fuels are called nonrenewable fuel sources. According to the Department of Energy, 85% of the total energy production in the U.S. comes from fossil fuels. Coal, petroleum, and natural gas can be used to create electricity. The amount of electricity used can be measured in kilowatt-hours (kwh). ➊ The table below shows the daily usage of electricity in households in several states. Complete the table by finding the amount of electricity used in one, four, and six weeks. Average Daily State Usage (kwh) Massachusetts 21 Illinois 26 Florida 37 Texas 41 California 19 Average Weekly Usage (kwh) Average 4-Week Usage (kwh) ➋ Find the difference between the least and greatest average 6-week usage. Average 6-Week Usage (kwh) ➌ Factors such as climate, lifestyle, and family size affect usage rates. Consumers in yearround temperate climates use less electricity for heating and cooling. Which state has the least average usage? What factors might influence that state s electric usage? ➍ Extension One gallon of oil produces about 15 kilowatt-hours of electricity. About how many gallons of oil would it take for a household s daily consumption of electricity in Illinois? Math and Science Activity 4 10

27 Name Vocabulary 1. A variable is a symbol or letter that stands for a number. Reteach to Build Understanding 4-11 Jimmy practices playing the piano for 30 minutes each day, 30 days each month. How many minutes does Jimmy practice playing the piano in one month? Complete the bar diagram. Write a multiplication equation for the bar diagram. Let p represent the number of minutes Jimmy practices each month. p minutes in one month 30 days p = 30 = Jimmy practices playing piano minutes in one month. Margie is training for a bike race. She rides her bike 12 miles every day. If there are 12 weeks until the race, how many miles will Margie ride before the race? 2. Make a plan to solve the problem. Step 1: First, use a bar diagram to help find the number of miles Margie rides in 1 week. d = = Step 2: Now, find the total miles Margie will ride in 12 weeks. m = = miles Margie rides each day d miles in 1 week m miles before the race 12 weeks Margie will ride miles before the race. 3. Cami performs 18 back handsprings during a routine. If she practices the routine 13 times, how many back handsprings does Cami perform? Draw a bar diagram and write an equation to solve. On the Back! 4. Yuri made 12 fruit bouquets as gifts. Each bouquet used 5 oranges, 4 apples, and 2 bananas. How many pieces of fruit did Yuri use to make all 12 fruit bouquets? R 4 11

28 Tic Tac Toe Partner Talk Share your thinking while you work. Get Started or For Each Round Get 20 squares in one color and 20 in another color. Get two number cubes for players to share. Get paper and a pencil. Take turns. Toss one cube. That is the number of tens in a two-digit number. Toss the other cube. That is the number of ones in the same two-digit number. Explain how to multiply that two-digit number by 26. Cover that product. If the answer is taken, lose your turn. Example 3 tens 5 ones Find Explain how to find each partial product, and how to add the partial products. How to Win The first player or team to cover a row, column, or diagonal in one of the four sections of the game board wins , , , ,638 1, ,066 1, ,664 1,118 1, , ,092 1, , , , , , If you have more time Play again! Center Game 4 11

29 Tic Tac Toe Partner Talk Share your thinking while you work. Get Started or For Each Round Get 20 squares in one color and 20 in another color. Get two number cubes for players to share. Get paper and a pencil. Take turns. Toss one cube. That is the number of tens in a two-digit number. Toss the other cube. That is the number of ones in the same two-digit number. If that number is less than 30, multiply by 57. If that number is between 30 and 50, multiply by 68. If that number is greater than 50, multiply by 79. Cover that product. If the answer is taken, lose your turn. Example 3 tens 5 ones 35 is between 30 and 50. Multiply by 68. Find Explain each step. How to Win The first player or team to cover a row, column, or diagonal in one of the four sections of the game board wins. 1,197 5,056 2,924 2,312 4, ,345 2,108 4,187 4, ,448 2, ,135 1,425 5,214 1,311 2,380 2,788 1,254 4,424 3,128 2,176 3,060 1,368 4, ,992 4, ,898 2,244 4,977 1,482 If you have more time Play again! Center Game 4 11