Area Models
Use an area model to solve: 23 × 15.
345
Solve using the break-apart method: 34 × 12.
408.
Solve using the standard algorithm: 21 × 31.
651
Solve: 47 × 36 using the standard algorithm.
1,692
Solve using any method: 52 × 18.
936
In an area model, what does each box represent?
Each box represents partial products based on place values.
What is the first step in the break-apart method (F.O.I.L)?
Break each number into its place values (e.g., tens and ones).
What happens when no regrouping is needed?
Each place value multiplies without carrying over any extra digits.
In the standard algorithm, what do you do when a product exceeds 9 in a place value?
Regroup by carrying over to the next place value.
What’s the product of 63 × 27 using the break-apart method?
1,701
True or False: Area models always break numbers into hundreds, tens, and ones.
False (it depends on the numbers being multiplied).
Solve: Break 45 × 13 into parts and calculate.
585 (40 × 10 = 400, 40 × 3 = 120, 5 × 10 = 50, 5 × 3 = 15; add all parts).
Solve: 32 × 21.
672
Solve using the standard algorithm: 59 × 24.
1,416
Solve using an area model: 38 × 14.
532
Solve using an area model: 42 × 16.
672
What is another name for the break-apart method?
Distributive property method; F.O.I.L method
What does the term "no regrouping" mean in multiplication?
No digits need to be carried over to the next place value.
What is the difference between regrouping and no regrouping?
Regrouping occurs when digits need to carry over to the next column; no regrouping means they don’t.
Use the standard algorithm with regrouping to solve: 85 × 46.
3,910
Why is an area model useful for multiplication?
It breaks the problem into smaller, manageable parts based on place value.
Why is it important to add all the partial products at the end?
To get the final product of the multiplication
Solve: 41 × 12 using the standard algorithm.
492
Solve: 76 × 45.
3,420
Solve using the break-apart method: 29 × 13.
377