Multiplication Facts: Use Patterns Home-School Connection Topic 2 Dear Family, Your child is learning to multiply using 0, 1, 2, 5, 9, and 10 as factors. Help him or her learn these multiplication facts by using patterns. Skip counting patterns can help your child with multiplication facts using 2, 5, or 10 as factors. For example, to find 2 7 or 7 2, skip count by 2s seven times. 2, 4, 6, 8, 10, 12, 14 7 2 = 14 Make or buy a set of multiplication flash cards, and play this game with your child. Penny Patterns Materials cards with multiplication problems where 0, 1, 2, 5, 9, and 10 are factors, 100 pennies Step 1 Mix the multiplication cards and place them facedown. Step 2 Player 1 turns over a card without Player 2 seeing it. Player 1 then uses pennies to show the multiplication problem. For example, if the problem is 4 5, Player 1 could place the pennies in 4 rows of 5 pennies each. Step 3 Player 2 looks at the penny pattern and says what multiplication problem is on the card and gives the answer. Observe Your Child After your child has created an array, have him or her skip count the pennies using one of the factors. Make clear that a pattern can also be observed by counting by the other factor.
Nombre Operaciones de multiplicación: Usar patrones De la escuela al hogar (en español) Tema 2 Estimada familia: Su niño(a) está aprendiendo a multiplicar usando 0, 1, 2, 5, 9 y 10 como factores. Ayúdelo(a) a aprender estas operaciones de multiplicación usando patrones. Los patrones para contar salteado pueden ayudar a su niño(a) con las operaciones de multiplicación usando 2, 5 o 10 como factores. Por ejemplo, para hallar 2 7 o 7 2, se cuenta de 2 en 2 siete veces. 2, 4, 6, 8, 10, 12, 14 7 2 = 14 Haga o compre un juego de tarjetas relámpago y juegue con su niño(a). Patrones de monedas de 1 Materiales tarjetas con problemas de multiplicación donde 0, 1, 2, 5, 9 y 10 son factores, 100 monedas de 1. Paso 1 Mezclen las tarjetas de multiplicación y pónganlas boca abjo. Paso 2 El jugador 1 voltea una tarjeta sin que el jugador 2 la vea. Luego, el Jugador 1 usa las monedas de 1 para mostrar el problema de multiplicación. Por ejemplo, si la multiplicación es 4 5, el Jugador 1 puede poner las monedas de 1 en 4 filas de 5 centavos cada una. Paso 3 El Jugador 2 mira el patrón de la moneda de 1, dice cuál es el problema de multiplicación de la tarjeta y da la respuesta. Observe a su niño(a) Luego de que su niño haya creado una matriz, pídale que cuente salteado usando uno de los factores. Dígale que también se puede observar un patrón contando con el otro factor.
Vocabulary 1. Multiples are the products of a number and other whole numbers. Complete each table. Multiples of 2 Multiples of 5 0 2 = 0 0 5 = 0 1 2 = 2 1 5 = 5 2 2 = 4 2 5 = 10 3 2 = 6 3 5 = 15 4 2 = 4 5 = 5 2 = 5 5 = 6 2 = 6 5 = Reteach to Build Understanding 2-1 2. List two more multiples of 2 and two more multiples of 5 that are not in the tables above. 3. Multiples of 2 always end with one of these digits:. 4. Multiples of 5 always end with one of these digits:. 5. You can skip count to find multiples of 2. Skip count the number of shoes in 4 pairs: 2, 4,,. 6. You can skip count to find multiples of 5. List the next 3 multiples of 5 by skip counting the number of cents in 5 nickels: 5 cents, 10 cents,,,. On the Back! 7. Alicia wants to show 8 5 using groups of counters. Each group will have 5 counters. Draw a picture of the groups of counters. How many counters will you draw to show this multiple of 5? R 2 1
Quick Questions Partner Talk Share your thinking while you work. Get Started or or For Each Question How to Win Each player tosses two number cubes. If your numbers match another player s numbers, toss again. Decide who will read the first question. Take turns. Listen to the reader. Discuss and agree on the correct answer. Every player who has that answer can remove one cube that shows the answer. The first player who removes both cubes wins. Have fun! a Multiply 5 9. Which digit is in n Multiply 1 2. Which digit is in b Multiply 5 4. Which digit is in o Multiply 9 5. Which digit is in c Multiply 7 5. Which digit is in p Multiply 7 5. Which digit is in d Multiply 3 5. Which digit is in q Multiply 2 7. Which digit is in e Multiply 9 5. Which digit is in r Multiply 3 2. Which digit is in f Multiply 6 5. Which digit is in s Multiply 5 6. Which digit is in g Multiply 2 8. Which digit is in t Multiply 7 2. Which digit is in h Multiply 5 5. Which digit is in u Multiply 5 2. Which digit is in i Multiply 8 5. Which digit is in v Multiply 5 5. Which digit is in j Multiply 6 2. Which digit is in w Multiply 5 7. Which digit is in k Multiply 3 5. Which digit is in x Multiply 2 3. Which digit is in l Multiply 8 2. Which digit is in y Multiply 2 9. Which digit is in m Multiply 2 6. Which digit is in z Multiply 6 2. Which digit is in If you have more time Toss two number cubes again. Play another game. Begin with the next question in the list. Center Game 2 1
Quick Questions Partner Talk Share your thinking while you work. Get Started or or For Each Question How to Win Each player tosses two number cubes. If your numbers match another player s numbers, toss again. Decide who will read the first question. Take turns. Listen to the reader. Discuss and agree on the correct answer. Every player who has that answer can remove one cube that shows the answer. The first player who removes both cubes wins. Have fun! a Which number times 7 equals 14? b One factor is 5. The product is 20. c Which number times 2 equals 6? d How many multiples of 2 are less than 20 and have a 1 in the tens place? n o p q How many multiples of 2 are less than 12? One factor is 2. The product is 2. One factor is 5. The product is 15. How many multiples of 5 are 1-digit numbers? e Which number times 2 equals 2? f How many multiples of 5 are less than 30? g One factor is 2. The product is 8. h 8 times which number equals 16? i How many multiples of 2 are 1-digit numbers? j Which number times 5 equals 5? k One factor is 2. The product is 12. l Which number times 5 equals 15? m One factor is 9. The product is 18. r How many multiples of 2 are less than 8? s t One factor is 5. The product is 5. One factor is 9. The product is 45. u How many multiples of 2 are less than 4? v One factor is 2. The product is 6. w How many multiples of 5 are less than 5? x y z One factor is 5. The product is 30. How many multiples of 5 are less than 20? One factor is 8. The product is 40. If you have more time Play another game. Begin with the next question in the list. Or make up your own questions like these. Play the game with your questions. Center Game 2 1
Vocabulary 1. Factors are the numbers that are multiplied together. The product is the answer to a multiplication problem. In the multiplication problem 9 3 = 27, is a factor, and is the product. is a factor, Reteach to Build Understanding 2-2 2. Look for patterns in the multiples of 9. Complete the table. As the multiples become greater, the tens digit increases by each row. in Multiples of 9 0 9 = 0 1 9 = 9 2 9 = 18 3 9 = 27 4 9 = 5 9 = 6 9 = 7 9 = 8 9 = 9 9 = As the multiples become greater, the ones digit decreases by each row. in The sum of the digits in the product of any 9s fact is always, unless one of the factors is 0. 3. The tens digit of any multiple of 9 is 1 than the factor that is multiplied by 9. 4. For 6 9, the tens digit of the multiple must be. 5. The product of 5 9 is. The two digits in the product are and. The sum of those two digits is. On the Back! 6. John wants to show 6 9 using groups of stars. Each group will have 9 stars. Draw a picture to show these groups of stars. How many stars will you draw to show this multiple of 9? R 2 2
Swinging Back and Forth Math and Science Activity 2-2 Did You Know? A pendulum is a weight that hangs from a point and can swing back and forth. The time it takes for a pendulum to swing back and forth depends on the length and weight of the pendulum and also the force of the push. A tire swing is one example of a pendulum. ➊ Josie pushes Max on a tire swing. Max swings for 9 seconds with each push. Complete the chart to show the amount of time Max swings with 1, 2, 3, 4, and 5 pushes. Push Swing Time ➋ How many pushes are needed for Max to swing at least 60 seconds? Explain. ➌ Extension How long will Max swing if Josie pushes him 10 times on the swing? Math and Science Activity 2 2
Vocabulary 1. The Identity (One) Property of Multiplication: When you multiply any number by 1, the product is that number. Reteach to Build Understanding 2-3 There is 1 muffin on each of 5 napkins. The multiplication equation for the number of muffins on the 5 napkins is: 1 =. 2. The Zero Property of Multiplication: When you multiply any number by 0, the product is 0. There are 0 muffins on each napkin. The multiplication equation for the number of muffins on the 6 napkins is: 0 =. 3. What product does the picture show? 4. What product does the picture show? 5. In the space below, draw a picture of counters that shows 9 1. On the Back! 6. Draw a picture that shows 8 0. How do you know the product will be 0? R 2 3
Vocabulary 1. Factors are numbers that are multiplied together to give a product. Multiples are the products of a number and other whole numbers. Look for patterns in the multiples of 10. Complete the table. Reteach to Build Understanding 2-4 Factors Multiples Factors Multiples 0 10 = 0 6 10 = 60 1 10 = 10 7 10 = 70 2 10 = 20 8 10 = 3 10 = 30 9 10 = 4 10 = 10 10 = 5 10 = All the multiples of 10 have a in the ones place. 2. Describe another pattern in the multiples of 10 table shown above. 3. What multiple of 10 do the stars show? 4. Draw groups of counters that represent 3 10. What multiple of 10 did you represent? On the Back! 5. Draw a number line to find the product of 7 10. R 2 4
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 the multiplication expression. Explain how to find the product. 7 10 10 2 6 9 3 2 8 4 5 10 5 10 9 6 7 10 8 8 10 9 10 6 10 9 9 11 8 9 12 5 6 90 81 70 16 80 54 60 100 30 100 90 80 70 72 50 60 How to Win You win if you are the first to get four connected rectangles, like: Center Game 2 4 If you have more time Play again!
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 Say each product. Tell which symbol you would use to compare the product on the left with the product on the right. 2 5 6 4 10 3 5 9 2 7 4 3 10 4 5 5 10 8 9 9 6 9 8 6 10 7 5 10 10 10 8 5 7 10 5 9 5 8 4 10 10 10 9 8 2 11 8 10 9 7 12 2 5 6 1 < < = > > < < > > = > < > < > < How to Win You win if you are the first to get four connected rectangles, like: Center Game 2 4 If you have more time Play again!
Reteach to Build Understanding 2-5 Vocabulary 1. You can use multiplication to solve problems with equal groups. Hannah buys 3 movie tickets. Each ticket is $9. Admit One $9 Admit One Multiply to solve the problem: =. 2. One way to solve a multiplication problem is to skip count. Andrew bought 6 packages with 5 pens in each package. Skip count by 5s to solve. 5,,,,, 6 5 = pens 3. You can show multiplication with a bar diagram. The bar diagram shows equal groups of.? 10 10 10 10 10 10 10 7 = 4. Array 1 shows: Array 1 Array 2 There are There are rows. counters in each row. 2 4 = Array 2 shows: There are There are rows. counters in each row. 4 2 = On the Back! 5. Show two ways to solve the problem. Liliana has 5 sheets of stickers. Each sheet has 9 stickers. How many total stickers does Liliana have? R 2 5
Vocabulary 1. You solve an equation by finding the value that is unknown. You can use a bar diagram to represent the unknown. Garrett gets $5 every time he mows the lawn. He mowed 2 times in June, 4 times in July, and 4 times in August. How much did Garrett earn from mowing? Fill in the unknown numbers in the bar diagrams and equations to solve. Reteach to Build Understanding 2-6 times Garrett mowed? money earned + + = = 2. Some problems have hidden questions. Logan bought 3 bottles of water during the field trip and Bill bought 2 bottles of water. Each bottle costs $2. How much did the boys spend on bottled water? Hidden Question: How many Logan and Bill buy on the field trip? 3. Complete the bar diagram and equation to solve the hidden question. 3 + = 4. Draw a bar diagram and complete the equation to solve the problem. $2 = did? bottles of water number of bottles Logan bought number of bottles Bill bought The boys spent on bottled water. On the Back! 5. Demitri has 3 posters. On each poster, there are 3 animal jokes, 2 sports jokes, and 4 knock-knock jokes. How many total jokes are on all of the posters? Use bar diagrams and equations to solve. R 2 6
Kicking a Ball Math and Science Activity 2-6 Did You Know? A soccer player s foot contains energy. When the foot hits the ball, the energy is released. The ball is in motion and it is headed to a new position. The speed the ball moves depends on the amount of force the player uses to kick the ball. How far the ball travels depends on how forceful or gentle the kick is. Lucas kicked a golf ball, a baseball, and a soccer ball. He kicked each ball 3 times. The distance the ball traveled after each kick is shown in the table below. Kick 1 Kick 2 Kick 3 golf ball 5 yards 5 yards 5 yards baseball 9 yards 9 yards 9 yards soccer ball 10 yards 10 yards 10 yards ➊ Draw a bar diagram to represent the total distance that the soccer ball was kicked. ➋ Draw a number line to represent the total distance that the soccer ball was kicked. ➌ What is the total distance that the soccer ball was kicked? ➍ Extension How many more yards did Lucas kick the soccer ball than the baseball? Show your work. Math and Science Activity 2 6