Mission 5 Summary
Mission 5 Summary
Embedded Files
Learning Objectives
Identify and generate equivalent fractions using visual models, such as fraction strips or number lines.
Relate unit fractions to other fractions by composing and decomposing them.
Convert improper fractions to mixed numbers and vice versa using models and number lines.
Compare fractions and mixed numbers by finding common denominators or using benchmark fractions.
Solve word problems involving addition and subtraction of fractions and mixed numbers using visual models and equations.
A given fraction is represented as repeated addition of unit fractions. It is same as multiplying that unit fraction by a whole number.
Example:
Use Area Model to represent Equivalent Fractions
Two different fractions are equivalent if they represent the same portion of a whole.
a. We can use multiplication to create an equivalent fraction that comprises smaller units.
Any unit fraction length can be partitioned into n equal lengths. For example, each third in the interval from 0 to 1 may be partitioned into 4 equal parts. Doing so multiplies both the total number of fractional units (the denominator) and the number of selected units (the numerator) by 4.
Example:
b. We can use division to create an equivalent fraction that comprises larger units.
In some cases, fractional units may be grouped together to form some number of larger fractional units.
For example, when the interval from 0 to 1 is partitioned into eights, one may
group 2 eights at a time to make fourths. By doing so, both the total number of
fractional units and number of selected units are divided by 2.
Example:
a. Use benchmarks and common units to compare fractions with different numerators and different denominators.
We reason that 4 sevenths is more than 1 half, while 2 fifths is less than 1 half.
∴ 4 sevenths is greater than 2 fifths.
b. Compare fractions using the same numerators.
i) The fraction with the greater denominator is the lesser fraction since the size of the fractional unit is smaller as the whole is decomposed into more equal parts.
Example:
ii) We can also make like numerators at times to compare.
Example:
c. Compare fractions using the same numerators.
Comparing fractions with related denominators.
We use this when one denominator is the factor of the other denominator.
d. Comparing fractions with unrelated denominators.
When the units are unrelated, we use area models and multiplication, whereby two fractions are expressed in terms of the same denominators.
a. Adding Fractions:
If the units are the same fractions can be added directly.
b. Subtracting fractions:
When we subtract fractions from 1 whole, the whole is decomposed into the same units as the part being subtracted.
c. Word Problem:
Create tape diagrams or number lines to represent and solve fraction addition and subtraction word problems.
Example:
Use decomposition and visual models to add and subtract fractions less than 1 to and from whole numbers.
Example:
Example:
Subtracting the fraction from 1 using a number bond and a number line.
Use Addition and Multiplication to build fractions greater than 1 and express them as mixed fractions.
Example:
Use Benchmark Numbers to Estimate Sums and Differences of Mixed Numbers
Example:
Adding Mixed Number to a Fraction
a. Use a number bond or arrow way to decompose a fraction to make 1.
b. Adding like units
Example: Ones with ones and tenths with tenths, to add two mixed numbers.
Subtracting a Fraction from a Mixed Number
a. Count back or up, subtract from 1, or take one out to subtract from 1.
b. Subtraction by decomposing the total into a whole number and a fraction greater than one to either subtract a fraction or a mixed number.
Use Associative Property to Multiply a Whole Number times a mixed Number.
Use Distributive Property to Multiply a Whole Number by a Mixed Number
Familiar Terms and Symbols
• =, <, > - Equal to, less than, greater than
• Compose: Change a smaller unit for an equivalent of a larger unit,
e.g., 2 fourths = 1 half, 10 ones = 1 ten; combining 2 or more numbers, e.g., 1 fourth + 1 fourth = 2 fourths, 2 + 2 + 1 = 5
• Decompose Change a larger unit for an equivalent of a smaller unit,
e.g., 1 half = 2 fourths, 1 ten = 10 ones; partition a number into 2 or more parts, e.g., 2 fourths = 1 fourth + 1 fourth, 5 = 2 + 2 + 1
• Equivalent fractions: Fractions that name the same size or amount
• Fraction: E.g., __1 3 , __2 3 , __3 3 , __4 3
• Fractional unit: E.g., half, third, fourth
• Multiple: Product of a given number and any other whole number
• Non-unit fraction: Fractions with numerators other than 1
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