Mental Math Madness
This happens when you multiply a dividend by 10, the quotient also gets multiplied by this number
What is 10?
Numbers that divide evenly with no remainder
What are compatible numbers?
The first step in short division
What is setting up the problem with the divisor outside and dividend inside?
This model helps visualize division by creating a rectangle
What is an area model? (A rectangle where the area is the dividend, one side is the divisor)
The first step in the partial quotients method
What is estimating how many times the divisor goes into the dividend?
If 56 ÷ 8 = 7, then 5,600 ÷ 8 = 700
What is 700?
Use compatible numbers to estimate 478 ÷ 6
Compatible numbers: 480 ÷ 6 = 80: What is about 80?
Solve 936 ÷ 8 using short division
What is 117? (9 ÷ 8 = 1 R1, 13 ÷ 8 = 1 R5, 56 ÷ 8 = 7)
Use an area model to solve 182 ÷ 14
182 ÷ 14 = 13
Break 182 into 140 + 42
140 ÷ 14 = 10
42 ÷ 14 = 3
10 + 3 = 13
Solve 252 ÷ 14 using partial quotients
252 ÷ 14 = 18
14 × 10 = 140, subtract: 252 - 140 = 112
14 × 8 = 112, subtract: 112 - 112 = 0
10 + 8 = 18
Basic fact: 72 ÷ 9 = 8, add three zeros
What is 8,000?
Is 90 a reasonable answer for 542 ÷ 6? Explain using estimation
Compatible numbers: 540 ÷ 6 = 90. Yes, 90 is reasonable.
Use divisibility rules to determine if 456 is divisible by 6
Yes, 456 is divisible by 6 because:
Last digit (6) is even
Sum of digits (4+5+6 = 15) is divisible by 3
Break 408 ÷ 12 using the Distributive Property
408 ÷ 12 = 34
Break 408 into 360 + 48
360 ÷ 12 = 30
48 ÷ 12 = 4
30 + 4 = 34
Use partial quotients to solve 585 ÷ 13
585 ÷ 13 = 45
13 × 40 = 520, subtract: 585 - 520 = 65
13 × 5 = 65, subtract: 65 - 65 = 0
40 + 5 = 45
10,000 ÷ 50 = 200 people per trip
What is 200?
A store has 60 muffins. Each box holds 8. About how many boxes?
Compatible numbers: 64 ÷ 8 = 8. What is about 8 boxes?
Explain how to check your work in short division
How to check work: Multiply the quotient by the divisor to get the original dividend
Explain three benefits of using area models in division
Benefits of area models:
Makes difficult division easier
Helps understand place value
Shows how division connects to multiplication
Explain why different students might use different partial quotients
Different students can use different multiples that work, as long as they correctly divide the dividend
If 6 × 4 = 24, then 24 ÷ 6 = 4
What is an inverse operation?
Explain three reasons why estimation is important in division
What are:
Check if the answer makes sense
Catch calculation errors
Solve problems quickly when an exact answer isn't needed
List all divisibility rules for numbers 2-10
Divisibility Rules:
2: Last digit is even (0, 2, 4, 6, 8)
3: Sum of digits divisible by 3
4: Last two digits divisible by 4
5: Last digit is 0 or 5
6: Divisible by both 2 and 3
8: Last three digits divisible by 8
9: Sum of digits divisible by 9
10: Last digit is 0
Demonstrate the Distributive Property for division using the formula
(a + b) ÷ c = (a ÷ c) + (b ÷ c)
(120 + 36) ÷ 12 = (120 ÷ 12) + (36 ÷ 12) = 10 + 3 = 13
Demonstrate solving 672 ÷ 21 using partial quotients, showing all steps
672 ÷ 21 = 32
21 × 30 = 630, subtract: 672 - 630 = 42
21 × 2 = 42, subtract: 42 - 42 = 0
30 + 2 = 32