Multiplying with 9 MAFS.3.OA.3.7 MAFS.3.OA.4.9

18 bars in boxes with 3 in each box Lesson Opening Solve the two problems below. Write the equation you used to solve the problem. If 18 granola bars are to be packed in boxes of 3, how many boxes are needed? If there are 20 bags of chips in a box and Tonya has 4 boxes how many bags of chips does she have? 18 bars in boxes with 3 in each box 3 x ____ = 18 or 18 ÷ 3 = 6 Six boxes are needed. 4 boxes (groups) of 20 bags 4 x 20 = 20 + 20 + 20 + 20 = (4 x 10) + (4 x 10) = 80 Tonya has 80 bags of chips.

Multiplying with 9 Write your 10s facts from 0 to 10: 0 × 10 = 1 × 10 = 2 × 10 = 3 × 10 = 10 × 10 =

Multiplying with 9 Multiplying by 10 and subtracting a group is a strategy you can use for a 9 fact. 9 x 7

I don’t know 9 x 7, but I do know 10 x 7. Multiplying with 9 Multiplying by 10 and subtracting a group is a strategy you can use for a 9 fact. 9 x 7 I don’t know 9 x 7, but I do know 10 x 7.

I don’t know 9 x 7, but I do know 10 x 7. Multiplying with 9 Multiplying by 10 and subtracting a group is a strategy you can use for a 9 fact. 9 x 7 I don’t know 9 x 7, but I do know 10 x 7.

I don’t know 9 x 7, but I do know 10 x 7. Multiplying with 9 Multiplying by 10 and subtracting a group is a strategy you can use for a 9 fact. 9 x 7 I don’t know 9 x 7, but I do know 10 x 7. 10 x 7 = 70

Multiplying with 9 Multiplying by 10 and subtracting a group is a strategy you can use for a 9 fact. 9 x 7 I don’t know 9 x 7, but I do know 10 x 7. 10 x 7 = 70 Now, I need to take away a group of 7.

9 x 7 Multiplying with 9 10 x 7 = 70 70 – 7 = 63 Multiplying by 10 and subtracting a group is a strategy you can use for a 9 fact. 9 x 7 I don’t know 9 x 7, but I do know 10 x 7. 10 x 7 = 70 Now, I need to take away a group of 7. 70 – 7 = 63

So, 9 x 7 = 63 Multiplying with 9 10 x 7 = 70 70 – 7 = 63 Multiplying by 10 and subtracting a group is a strategy you can use for a 9 fact. So, 9 x 7 = 63 I don’t know 9 x 7, but I do know 10 x 7. 10 x 7 = 70 Now, I need to take away a group of 7. 70 – 7 = 63

= 27 = 54 = 72 = 63 = 81 Multiplying with 9 9 groups of 3 (9 x 3) So, what is… 9 groups of 3 (9 x 3) 9 groups of 6 (9 x 6) 9 groups of 8 (9 x 8) 9 groups of 7 (9 x 7) 9 groups of 9 (9 x 9) = 27 Think: 10 × 3 = 30, now subtract a group of 3, 30 – 3 = … = 54 Think: 10 × 6 = 60, now subtract a group of 6, 60 – 6 = … = 72 Think: 10 × 8 = 80, now subtract a group of 8, 80 – 8 = … Encourage students to model each problem, or use the doubling strategy they learned today. = 63 Think: 10 × 7 = 70, now subtract a group of 7, 70 – 7 = … = 81 Think: 10 × 9 = 90, now subtract a group of 9, 90 – 9 = …

Multiplying with 9 Let’s look at our Multiplication Table…

Multiplying with 9 Find all the multiples of 9… The ones place has a pattern that decreases by 1: 9, 8, 7, 6, 5, 4… The tens place has a pattern that increases by 1: 0, 1, 2, 3, 4, 5…

Multiplying with 9 Let’s look at our 100 Chart…

Multiplying with 9 Look at the multiples of 9… There is one multiple of 9 in every row, except in the case of 81 and 90. There is an even and an odd digit in the multiples of 9. The sum of the digits is 9.

Patterns in the Multiples of 9 9 x 0 = 9 x 1 = 9 x 2 = 9 x 3 = 9 x 4 = 9 x 5 = 9 x 6 = 9 x 7 = 9 x 8 = 9 x 9 = 9 x 10 = 9 1 8 2 7 The ones place decreases in number. 3 6 4 5 5 4 The tens place increases in number. 6 3 7 2 8 1 9

Patterns on the Multiplication Table What patterns do you notice on this table? Even numbers have multiples that are always even. Odd numbers… have multiples that are even, odd, even, odd… Check whether the multiples of a given factor are always even, always odd, or sometimes even & sometimes odd Multiples of… ALWAYS EVEN ALWAYS ODD SOMETIMES EVEN SOMETIMES ODD 2  5  6  7  10 

Nine Cross What each player needs: Nine Cross game board 2 sets of 0-10 cards (per partnership) How to play: One player selects a card from the deck, multiplies by 9, and records the product on their game board (in the correct row or column). The second player does the same thing except records the product on his/her own game board. The first player to complete a row OR column wins.

What is one strategy you used for multiplying with 9? Closing What is one strategy you used for multiplying with 9? Multiply by 10 then take away a group Use the patterns in the 9s facts Draw it/model it Use a tool (100 chart, multiplication chart)

Bonus Question Use your knowledge of the patterns in the 9s facts to help you answer the question below. Part of a multiplication table is shown. What numbers go in the empty cells? 50, 62, 71, 81 54, 63, 74, 81 54, 63, 72, 84 54, 63, 72, 81 42 48 60 49 56 70 64 80 63 72 90 The product can never be odd, because when you are multiplying any number by 2, you double the number. Anytime you double a number that number has a pair. If there is a pair, then it is not odd, it is always even. Have students model multiplying numbers by 2 (e.g. with unifix cubes). When students multiply 2 by 3, they make 2 sets of 3 (so there is a pair of 3). When there is a pair of numbers, the total has to be even.

Exit Ticket The auditorium at Sunrise Elementary has 9 rows of seats with 8 seats in each row. How many seats are in the auditorium? Model the problem. Write an equation that corresponds to it. Write another equation that corresponds to it. Write the answer to the problem in a complete sentence.