Mathematics
Grade 7
15 min
Model decimals and fractions (Tutorial Only)
Model decimals and fractions (Tutorial Only)
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Model fractions using visual representations like area models and number lines.
Model decimals using visual representations like base-ten grids and number lines.
Convert fractions to decimals and decimals to fractions using visual models.
Compare and order decimals and fractions using visual models.
Identify equivalent fractions and decimals through visual modeling.
Explain the relationship between place value and decimal representation in models.
Ever wonder how to visually show that 0.5 is the same as 1/2? 🤔 Let's explore how to draw and understand these connections!
In this tutorial, you'll learn to use various visual tools like grids, number lines, and area models to represent decimals and fractions. Understanding these models will help yo...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number representing a part of a whole, written as a ratio of two integers, numerator over denominator.In 3/4, 3 is the numerator (parts chosen), and 4 is the denominator (total parts).
DecimalA number that uses a decimal point to represent parts of a whole, based on powers of ten.0.75 represents seventy-five hundredths.
Visual ModelA diagram, drawing, or physical representation used to illustrate mathematical concepts.A 10x10 grid shaded to show 0.25.
Area ModelA visual model that uses a shape (like a rectangle or circle) divided into equal parts to represent fractions or decimals.A circle divided into 8 equal slices, with 3 shaded to show 3/8.
Number LineA straight line with numbers placed at equal intervals, used to represent and compare numbers.A number...
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Core Formulas
Fraction to Decimal Modeling
To model a fraction $\frac{a}{b}$ as a decimal, divide a whole into $b$ equal parts and consider $a$ of them. For a base-10 grid, find an equivalent fraction with a denominator of 10, 100, or 1000.
This rule helps you understand that a fraction represents a division. When modeling, you visually perform this division by splitting a whole into the denominator's number of parts and then considering the numerator's number of those parts. To model on a 10x10 grid, you often need to find an equivalent fraction first.
Decimal to Fraction Modeling
To model a decimal, identify its place value. For example, $0.d_1d_2$ means $d_1$ tenths and $d_2$ hundredths, which can be written as $\frac{d_1d_2}{100}$. In general, $0.d_1d_2...d_n = \frac{d_1d_2......
5 more steps in this tutorial
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Challenging
A student creates a number line from 0 to 1 but makes the mark for 0.5 much closer to 1 than to 0. They then place a point at the 0.5 mark to represent 1/2. Which statement best describes the student's error?
A.The student correctly placed 1/2, as its location is arbitrary.
B.The fraction 1/2 is not equal to 0.5, which is the source of the error.
C.The model is flawed because the divisions on the number line are not at equal intervals.
D.The student should have used an area model, as fractions cannot be shown on number lines.
Challenging
Which of the following fractions can be modeled perfectly by shading a whole number of squares on a 10x10 grid?
A.1/3
B.7/20
C.5/8
D.1/6
Challenging
A 10x10 grid represents a garden. 1/4 of the garden is planted with tomatoes. Of the remaining area, 1/3 is planted with peppers. What decimal represents the portion of the garden that has nothing planted in it?
A.0.25
B.0.33
C.0.75
D.0.50
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