Multiplying tenths by tenths with area models on a hundredths grid, a whole number times a decimal with one grid per group, and sharing hundredths into equal groups.
Shade one factor as columns, the other as rows. The squares shaded both ways are the product, in hundredths: 0.3 × 0.4 crosses 12 squares, so 0.12.
area modela rectangle whose area is the product
factora number being multiplied
productthe answer to a multiplication
hundredthone square of the grid: 0.01
Watch for: Counting all the shaded squares, not just where they cross. Writing 0.12 as 1.2 or 12. Thinking a product is always bigger than its factors.
At home: Draw a 10 × 10 grid and shade 0.5 × 0.6. Count the crossed squares together.
Sample sheet and answer key
Luna's Space Adventure
Grade 5 · Decimal area models · 5.3D
NameDate
Astronaut Luna is exploring a far-off corner of space. Solve each problem to help Luna's mission go smoothly!
Read the model
Count the squares shaded twice, where the columns and rows cross: each is one hundredth.
0.9 × 0.5 =
0.7 × 0.8 =
0.6 × 0.5 =
Draw the model
Shade the first factor in columns and the second in rows. Count where they cross.
0.4 × 0.7 =
0.5 × 0.9 =
0.2 × 0.9 =
Groups of a decimal
Each grid is one group. Add up the shaded squares.
2 × 0.25 =
2 × 0.16 =
Grade 5 · Sheet
Luna's Space Adventure
Grade 5 · Decimal area models · 5.3D
Answer key
Astronaut Luna is exploring a far-off corner of space. Solve each problem to help Luna's mission go smoothly!
Read the model
Count the squares shaded twice, where the columns and rows cross: each is one hundredth.
0.9 × 0.5 =0.45
0.7 × 0.8 =0.56
0.6 × 0.5 =0.3
Draw the model
Shade the first factor in columns and the second in rows. Count where they cross.
0.4 × 0.7 =0.28
0.5 × 0.9 =0.45
0.2 × 0.9 =0.18
Groups of a decimal
Each grid is one group. Add up the shaded squares.
2 × 0.25 =0.5
2 × 0.16 =0.32
Answer key
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New problems every time, three levels (gentle, core and stretch), themes to pick from, a second page if you want one. Each sheet comes with an answer key and a one-page guide for grown-ups.
