Mathematics 10. Add and subtract fractions and mixed numbers with unlike denominators, using fraction equivalence to calculate a sum or difference of fractions or mixed numbers with like denominators.
Unpacked Content
Evidence Of Student Attainment:
Students:
Use a variety of strategies and fraction equivalence to find sums and differences of fractions and mixed numbers with unlike denominators. Teacher Vocabulary:
Fraction
Denominator
Numerator
Visual Model
Sum
Difference
Equivalence
Unlike denominators
Unlike units Knowledge:
Students know:
Strategies to determine if two given fractions are equivalent.
How to use a visual model to illustrate fraction equivalency.
Contextual situations for addition and subtraction. Skills:
Students are able to:
Use fraction equivalence to add and subtract fractions and mixed numbers with unlike denominators. Understanding:
Students understand that:
Addition and subtraction of fractions and mixed numbers with unlike units,
Require strategies to find equivalent fractions in a common unit, and the sum or difference will be expressed in the common unit. Can be assessed for reasonableness of answers using estimation strategies. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.5.10.1: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
M.5.10.2: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
M.5.10.3: Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
M.5.10.4: Recognize and generate simple equivalent fractions.
M.5.10.5: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
M.5.10.6: Compare two fractions with the same numerator or the same denominator by reasoning about their size.
M.5.10.7: Recall basic addition, subtraction, multiplication, and division facts.
Prior Knowledge Skills:
Use fraction equivalence to add and subtract fractions and mixed numbers with unlike denominators.
Mathematics 12. Apply and extend previous understandings of multiplication to find the product of a fraction times a whole number or a fraction times a fraction.
a. Use a visual fraction model (area model, set model, or linear model) to show (a /b q and create a story context for this equation to interpret the product as a parts of a partition of q into b equal parts.
b. Use a visual fraction model (area model, set model, or linear model) to show (a /b c /d
c. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
d. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths to show that the area is the same as would be found by multiplying the side lengths.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a fraction times a whole number,
use visual models to illustrate the product to develop the procedure (a/b) × q.
Create a story context for the equation (a/b) × q. Given a fraction times a fraction,
Use visual models to illustrate the product to develop the procedure (a/b) × (c/d).
Create a story context for the equation (a/b) × (c/d).
Given a rectangle with two fractional side lengths,
Use an area model to illustrate and find the rectangular area.
Find the area by tiling it with unit squares of the appropriate unit fraction.
Given a rectangle with fractional side lengths including mixed numbers,
Use an area model to illustrate and find the rectangular area to lead to answers in the form of whole numbers or mixed numbers.
Use an area model to find the area of a rectangle by tiling the rectangle with unit squares.
Teacher Vocabulary:
Fraction
Fraction model
Whole number
Area
Area model
Linear model
Set model
Tiling
Unit squares
Equation Knowledge:
Students know:
How to write an equation involving repeated addition with fractions as a multiplication equation of a whole number times the fraction.
The relationship of partial products to an area model when multiplying by two whole numbers.
Area of a rectangle is determined by multiplying side lengths and is found in square units. Skills:
Students are able to:
Use previous understandings of multiplication to
Find products of a fraction times a whole number and products of a fraction times a fraction.
Use area models, linear models or set models to represent products.
Create a story context to represent equations (a/b) × q and (a/b) × (c/d) to interpret products.
Find area of rectangles with fractional side lengths and represent products as rectangular areas.
Find the area of a rectangle by tiling the area of a rectangle with unit squares. Understanding:
Students understand that:
Any whole number can be written as a fraction.
The general rule for multiplication involving fractions can be justified through visual models.
A variety of contextual situations can be represented by multiplication involving fractions.
Tiling with unit squares can be used to find the area of a rectangle with fractional side lengths. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.5.12.1: Define proper fraction.
M.5.12.2: Multiply fractions using denominators between 2 and 5.
M.5.12.3: Identify proper and improper fractions.
M.5.12.4: Recall basic multiplication facts.
M.5.12.5: Model changing a whole number to a fraction.
M.5.12.6: Partition a rectangle into rows and columns of same-size squares, and count to find the total number of them.
M.5.12.7: Label the numerator and denominator of a fraction.
M.5.12.8: Count the area squares for the length and width.
M.5.12.9: Identify the width and length of a rectangle.
Prior Knowledge Skills:
Solve real-word problems involving multiplication of fractions and mixed numbers.
Write equations to represent the word situation.
Use visual fraction models to represent the problem.
Alabama Alternate Achievement Standards
AAS Standard:
