Seeing multiplication as resizing: multiplying by more than 1 makes a number bigger, by less than 1 makes it smaller, and by exactly 1 keeps it the same.
Don't multiply. Look at the fraction: a top bigger than the bottom is more than 1, a smaller top is less than 1, and the same top and bottom is exactly 1.
factora number being multiplied
scalemake bigger or smaller by multiplying
more than 1a fraction with its top bigger than its bottom
equal to 1the same top and bottom, like 2/2
Watch for: Thinking multiplying always makes a number bigger. Missing that 2/2 is equal to 1, so 2/2 × 49 is just 49. Working out the whole product when only a comparison is needed.
At home: Before cooking, ask: if we make 1/2 of the recipe, will we need more flour or less? What about 1 1/2 times the recipe?
Sample sheet and answer key
Luna's Space Adventure
Grade 5 · Multiplying as scaling · 5.NF.B.5
NameDate
Astronaut Luna is exploring a far-off corner of space. Solve each problem to help Luna's mission go smoothly!
Bigger or smaller?
Don't multiply. Is the factor more than 1, less than 1, or 1?
4/3 × 29 isless than 29equal to 29more than 29
2/2 × 41 isless than 41equal to 41more than 41
3/4 × 20 isless than 20equal to 20more than 20
9/10 × 46 isless than 46equal to 46more than 46
7/8 × 50 isless than 50equal to 50more than 50
1/1 × 56 isless than 56equal to 56more than 56
4/3 × 75 isless than 75equal to 75more than 75
5/2 × 45 isless than 45equal to 45more than 45
3/4 × 89 isless than 89equal to 89more than 89
1/1 × 41 isless than 41equal to 41more than 41
1/1 × 77 isless than 77equal to 77more than 77
3/2 × 35 isless than 35equal to 35more than 35
Sheet
Luna's Space Adventure
Grade 5 · Multiplying as scaling · 5.NF.B.5
Answer key
Astronaut Luna is exploring a far-off corner of space. Solve each problem to help Luna's mission go smoothly!
Bigger or smaller?
Don't multiply. Is the factor more than 1, less than 1, or 1?
4/3 × 29 isless than 29equal to 29more than 29
2/2 × 41 isless than 41equal to 41more than 41
3/4 × 20 isless than 20equal to 20more than 20
9/10 × 46 isless than 46equal to 46more than 46
7/8 × 50 isless than 50equal to 50more than 50
1/1 × 56 isless than 56equal to 56more than 56
4/3 × 75 isless than 75equal to 75more than 75
5/2 × 45 isless than 45equal to 45more than 45
3/4 × 89 isless than 89equal to 89more than 89
1/1 × 41 isless than 41equal to 41more than 41
1/1 × 77 isless than 77equal to 77more than 77
3/2 × 35 isless than 35equal to 35more than 35
Answer key
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.
