Multiplying two fractions using models

An area model turns a product of fractions into a count. Columns show the first fraction, rows show the second, and the cells shaded twice are the answer, over the total number of cells. The page spells this out in five steps on 1/7 × 4/6: 4 overlapping cells out of 6 × 7 = 42.

It also says do not simplify, on purpose. Count, do not compute. Keeping 4/42 instead of 2/21 lets the numerator stay a number your child can point to.

Later grids get bigger, 12 by 6 and 8 by 8, so counting gives way to multiplying rows by columns. The standard is 5.NF.B.4.b: finding area by tiling and showing it matches the product of the side lengths.

Point at problem 3 and ask, "How many columns? How many rows?" Count them. Twelve and six make 72 cells, and 55 of them carry both colors.

One correction for you: the answer key prints 55/132 for problem 3. The model has 72 cells, so the product is 55/72.

The pages are also out of order in the file. The first sheet holds the example with problems 1 and 2, the last sheet holds problems 3 to 6, and the two middle sheets are answers, so print the first and last for your child. Problems 5 and 6 show the product but no grid: your child draws a 5-by-7 rectangle and a 5-by-2 rectangle, then shades them.

Graph paper turns any recipe into an area model. Half of 3/4 cup of milk: draw 4 columns and 2 rows, shade 3 columns and 1 row, and your child counts 3 of 8 cells before pouring 3/8 cup.

In the garden, a bed that is 2/3 planted, with half of that in tomatoes, makes a model to sketch in the dirt. What fraction of the bed holds tomatoes? One third.

Spaghetti and Meatballs for All! by Marilyn Burns pushes square tables together for a family reunion, a friendly way into grids and area.

Let your child hear what counted: "You found the overlap before you counted it." Word problems with fraction multiplication come next.