ALEX Classroom Resource

Students:

• Model and solve real-world problems involving sums and differences of fractions (including mixed numbers) with unlike denominators.
• Use visual models to illustrate the problem situation involving fractions.
• Use fraction understanding and estimation strategies to assess the reasonableness of answers.

Students know:

• The meaning and magnitude of fractions expressed in units of halves, fourths, eighths, thirds, sixths, twelfths, fifths, tenths, and hundredths.
• Strategies to find sums of two or more fractions with like denominators.
• Strategies to find the difference of two fractions with like denominators.
• How to decompose a fraction greater than 1 and express as a mixed number.
  Example: 7/3 = 3/3 + 3/3 + 1/3 = 2 1/3.

Students are able to:

• Solve real-word problems involving addition and subtraction of fractions with unlike denominators.
• Represent problems using fraction models or equations.
• Assess reasonableness of answers using estimation and benchmark fractions.

Students understand that:

• solving word problems involving addition and subtraction of fractions 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.

Learning Objectives:
M.5.9.1: Add and subtract mixed numbers with like denominators.
M.5.9.2: Recognize that comparisons are valid only when the two fractions refer to the same whole.
M.5.9.3: Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
M.5.9.4: Recognize a fraction as a number on the number line; represent fractions on a number line diagram.
M.5.9.5: Recognize key terms to solve word problems.
M.5.9.6: Apply properties of operations for addition and subtraction.
M.5.9.7: Recall basic addition and subtraction facts.

Students:

• Use a variety of strategies and fraction equivalence to find sums and differences of fractions and mixed numbers with unlike denominators.

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.

Students are able to:

• Use fraction equivalence to add and subtract fractions and mixed numbers with unlike denominators.

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.

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.

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.

Example: Using an area model, a rectangle with dimensions of 1 1/2 x 1 2/3 will have partial products of 1, 1/2, 1/3, and 1/6 and the sum of the partial products will give an area of 2 sq units.
• Use an area model to find the area of a rectangle by tiling the rectangle with unit squares.

Example: Using an area model, a rectangle with dimensions 1 1/2 x 1 1/3 will be tiled with unit squares of 1/6 size showing the tiled partial products as 6/6, 3/6, 2/6, and 1/6 for a total area of 12/6 sq units, so it would take 12 tiles of size 1/6 units to cover the area of the rectangle.

Students know:

• How to write an equation involving repeated addition with fractions as a multiplication equation of a whole number times the fraction.
  Example: 2/9 + 2/9 + 2/9 + 2/9 = 4 x 2/9 = 8/9.
• 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.

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.

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.

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.

Students:

• Use a variety of strategies, including models, pictures, tables, and patterns to solve problems that provide a context for multiplying fractions and mixed numbers.

Students know:

• Contextual situations for multiplication.
• How to use an area model to illustrate the product of two whole numbers and its relationship to partial products and extend this knowledge to illustrate products involving fractions and mixed numbers.

Students are able to:

• 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.

Students understand that:

• A variety of strategies are used to model and solve problems that provide a context for multiplying fractions and mixed numbers.
• Solutions are interpreted based on the meaning of the quantities and the context of the problem situation.

Learning Objectives:
M.5.14.1: Define improper fraction, mixed number, fraction, equations, numerator, denominator.
M.5.14.2: Multiply proper fractions with common denominators 2-10.
M.5.14.3: Solve problems using whole numbers.
M.5.14.4: Write number sentences for word problems.
M.5.14.5: Identify key terms to solve multiplication word problems.
Examples: times, every, at this rate, each, per, equal/equally, in all, total.
M.5.14.6: Recall basic multiplication facts.