Multiplication Strategies
True or False: 30 x 9 = 9 x (10+3)
False
What is 12 × 9?
108
If you divide 45 ÷ 6, how many times does 6 go in 45 and what is the remainder?
7 times, remainder 3
In a ratio table if 5 × 4 = 20, what is 50 × 4?
200
If one notebook costs $4 and you buy 7 notebooks, how much do you spend?
$28
If 7 × 6 = 42, then 70 × 6 = ___?
420
Calculate 34 × 12.
408
A baker has 1,234 muffins and puts them into boxes of 12. How many full boxes can he fill and how many muffins remain?
102 full boxes (since 102×12=1,224), remainder 10 muffins
If one student has 8 pencils and another has 24 pencils, how many times more does the second student have?
3 times as many.
A factory produces 345 widgets each day. How many widgets in 30 days?
10,350.
Describe how an area model can help you multiply 23 × 15.
You break 23 into 20 + 3 and 15 into 10 + 5, draw a rectangle with parts, multiply each part, then add results.
What is 456 × 7?
3,192
46 ÷ 8.
5 r 6
Fill in the ratio table:
| 2 | 10 | ? |
| 5 | ? | 35|
Then the table entries: top row: 2,10,14; bottom row:5,25,35.
A school orders 2,158 pencils. They pack them in boxes of 24. How many full boxes and how many pencils left over?
89 boxes (since 24×89=2,136) remainder 22 pencils
Multiply 1,200 × 30 using multiples of 10 and 100s.
36,000
123 × 46
5,658
Explain how multiplication helps you check a division with remainder.
Multiply the divisor by the quotient, then add the remainder; the result should equal the original dividend.
A car travels 270 miles in 3 hours. At that rate, how far does it travel in 10 hours?
900 miles
For a fundraiser you make bags of candy: each bag has 56 pieces. If you have 2,300 pieces, how many full bags can you make and how many pieces remain?
41 bags (since 56×41=2,296) remainder 4 pieces
Explain how you would multiply a 3-digit number by a 2-digit number using place-value reasoning (not just the algorithm).
For example, 234 × 56 = (200 × 56) + (30 × 56) + (4 × 56), compute each, then add.
Multiply 2,304 × 25
57,600
Divide 578 ÷ 10. What is the quotient and remainder?
57r8
Write a multiplicative comparison for this scenario: “Jenny has 9 times as many marbles as Mike. Mike has 46 marbles. How many marbles does Jenny have?” Then solve.
Jenny has 9 × 46 = 414 marbles.
A rectangular garden is 48 m long and 23 m wide. How many square meters is the area? If 8 m² of soil costs $6, estimate the cost to buy soil for the entire garden (round as needed).
Area = 48 × 23 = 1,104 m². Soil cost per 8 m² = $6 → cost per m² = $6/8 = $0.75. So estimated cost = 1,104 × 0.75 = $828