Worksheet: Multiplying Two-Digit Numbers by One-Digit Numbers: Area Models

In this worksheet, we will practice using area models to multiply two-digit numbers by one-digit numbers.

Q1:

Amelia drew this to help her calculate 3×17.

What expression is missing in the following: 3×17=3×(10+7)=(3×10)+()?

  • A7×10
  • B3×3
  • C3×10
  • D3×7

What is 3×17?

Q2:

Mason is learning to multiply by breaking apart factors and then adding.

For 6×12, he draws a 6-by-12 rectangle and splits it into two parts.

What is the missing expression in 6×12=()+(6×4)?

  • A6×7
  • B6×8
  • C6×10
  • D6×9

What is 6×12?

Q3:

Anthony and Olivia want to use area to find 6×14.

Olivia splits this rectangle in half, but she can’t finish because she doesn’t know 6×7.

Anthony says it is easier to use the 10 times table. How would he split the rectangle?

  • A
  • B

Pick the next step in Anthony’s calculation.

  • A(6×10)+(6×4)
  • B(6×10)+4
  • C(6×8)+6
  • D(6×8)+(6×6)

Add the areas of the two parts to figure out 6×14.

Q4:

Elizabeth used 9=101 to find 9×15.

9×15=(101)×15=(10×15)(1×15)

Liam used 15=10+5 to find 9×15.

9×15=9×(10+5)=(9×10)+(9×5)

Whose method is correct?

  • AThey are both wrong.
  • BThey are both correct.
  • COnly Elizabeth’s method is correct.
  • DOnly Liam’s method is correct.

What is 9×15?

Q5:

Jacob has drawn this to help him multiply 3 and 18.

Pick the equation that describes his model.

  • A3×18=(3×20)2
  • B3×18=3×(9+2)
  • C3×18=3×(20+2)
  • D3×18=3×(202)

Use the model to write the subtraction expression that is missing: 3×18=.

  • A60+6
  • B266
  • C606
  • D602

What is 3×18?

Q6:

Sophia has drawn this array to help her calculate 7×12 by splitting 12 into 10+2.

There are 7×10 squares in the blue part. Write an expression for the number of squares in the pink part.

  • A7×2
  • B7+2
  • C10×2
  • D10+2

Which of these is equal to 7×12?

  • A(7×10)(7×2)
  • B(7×10)+(10×2)
  • C(7×10)(10×2)
  • D(7×10)+(7×2)

Which expression correctly shows the total number of squares in the array?

  • A7014=56
  • B7020=50
  • C70+14=84
  • D70+20=90

Q7:

This area model can be used to solve 85×9.

Find the missing partial product.

Q8:

Find the area of the rectangle using the distributive property.

Q9:

William drew this array to help him calculate 4×15 by splitting 15 into 10+5.

How many squares are in the orange part?

  • A60
  • B15
  • C40
  • D20

How many squares are in the green part?

  • A15
  • B20
  • C40
  • D60

Add these numbers to find 4×15.

  • A40
  • B60
  • C20
  • D80

Q10:

A teacher has 34 children in her class. They each need 7 pieces of homework a week. By using the diagram, find how many pieces she will have to set altogether.

Q11:

Liam drew this to help him multiply 6 by 18.

Pick the equation that shows how he split 18.

  • A6×18=6×(9+2)
  • B6×18=6×10×8
  • C6×18=6×(10+8)
  • D6×18=6×5×4

Which expression should he write for the number of orange squares?

  • A8×10
  • B6×8
  • C6×10
  • D6×9

Which two numbers can he add to find 6×18?

  • A30+48
  • B54+48
  • C60+48
  • D60+30

Q12:

Charlotte drew this to help her multiply 4 and 23.

Pick the equation that shows how she split 23.

  • A4×23=4×(20+3)
  • B4×23=4×(19+4)
  • C4×23=4×(20+4)
  • D4×23=4×(19+2)

She can add the areas of the two parts to find 4×23.

Write the sum she should do.

  • A76 + 8
  • B80 + 8
  • C80 + 13
  • D80 + 12

What is 4×23?

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