Mathematics
Grade 7
15 min
Multiply two decimals using grids
Multiply two decimals using grids
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Introduction & Learning Objectives
Learning Objectives
Represent decimals (tenths) on a 10x10 grid.
Model the multiplication of two decimals using an overlapping grid method.
Identify the product of two decimals by counting the double-shaded squares on a grid.
Relate the grid model to the concept of area for decimal multiplication.
Explain why the grid method visually demonstrates decimal multiplication.
Solve simple real-world problems involving decimal multiplication using grid models.
Ever wondered how much space a small rug takes up if its sides are measured in parts of a meter? 📏 Let's find out how grids can help us visualize these calculations!
In this lesson, you'll learn a powerful visual method called the area grid model to multiply two decimals. This method helps you understand why multi...
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Key Concepts & Vocabulary
TermDefinitionExample
DecimalA number that includes a whole number part and a fractional part, separated by a decimal point. It represents parts of a whole.0.75, 2.3, 0.1
Grid Model (Area Model)A visual representation, often using squares, to show multiplication as finding the area of a rectangle. For decimals, a 10x10 grid typically represents one whole.A 10x10 grid where each small square is 0.01.
FactorA number that is multiplied by another number to find a product.In the multiplication $0.5 imes 0.3$, both $0.5$ and $0.3$ are factors.
ProductThe result obtained when two or more numbers are multiplied together.In $0.5 imes 0.3 = 0.15$, the number $0.15$ is the product.
TenthsThe first place value to the right of the decimal point, representing fractions with a denominator of 10.In $0...
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Core Formulas
Representing Decimals on a Grid
To represent a decimal $0.X$ (where $X$ is a digit from 0-9) on a 10x10 grid, shade $X$ full columns or $X$ full rows.
Each small square in a 10x10 grid represents $0.01$. A full column or row represents $0.1$. Therefore, $0.X$ represents $X$ tenths, which is equivalent to $X$ columns or rows of 10 squares each.
Modeling Multiplication with Overlapping Grids
For the product $0.X \times 0.Y$, represent $0.X$ by shading $X$ columns vertically with one color, and represent $0.Y$ by shading $Y$ rows horizontally with another color on the same 10x10 grid.
This process creates an area model where the dimensions of the rectangle are the two decimal factors. The intersection of these two shaded areas forms a new rectangle whose area is the product....
5 more steps in this tutorial
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Challenging
The overlapping region of a grid model for 0.A × 0.B consists of 12 squares. If A and B are different single-digit whole numbers, which of the following pairs is NOT a possible set of factors?
A.0.2 and 0.6
B.0.3 and 0.4
C.0.1 and 1.2
D.0.4 and 0.3
Challenging
When multiplying two decimals in the tenths place, like 0.A × 0.B, using a 10x10 grid, why is the product always in the hundredths place?
A.Because you are multiplying tenths by tenths, which results in hundredths (1/10 × 1/10 = 1/100).
B.Because the grid always has 100 squares, the answer must have two decimal places.
C.Because you always add the number of decimal places in the factors.
D.It is not always in the hundredths place; it can be in the tenths place.
Challenging
Imagine you want to model 1.2 x 0.3 using a similar grid method. How could you represent the factor 1.2?
A.It's impossible to model numbers greater than 1.
B.Shade 12 columns on a single 10x10 grid.
C.Use one fully shaded 10x10 grid and 2 shaded columns on a second 10x10 grid.
D.Shade 1 column on one grid and 2 columns on a second grid.
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