In this video segment from Cyberchase, Harry gets a new job as the manager of a candy store. Customers who come into the store use fractions to order boxes of different types of chocolates. Harry teaches his cousin, Harley, how the fractional amounts correspond to the number of pieces to place in the box. Harley takes over during Harry’s lunch break, and when Harry returns he finds a disappointed customer was not given the correct amount of chocolates in his order.

Content Standard(s):

Mathematics MA2019 (2019) Grade: 4

16. Apply and extend previous understandings of multiplication to multiply a whole number times a fraction.

a. Model and explain how a non-unit fraction can be represented by a whole number times the unit fraction.

Example:^{9}/_{8}=9 x ^{1}/_{8}

b. Extend previous understanding of multiplication to multiply a whole number times any fraction less than one.

Example: 4 x ^{2}/_{3}= ^{4 x 2}/_{3}= ^{8}/_{3}

c. Solve word problems involving multiplying a whole number times a fraction using visual fraction models and equations to represent the problem._{}

Examples: 3 x ^{1}/_{2}, 6 x ^{1}/_{8}

Unpacked Content

Evidence Of Student Attainment:

Students:

Model and explain a fraction as a multiple of a unit fraction.

Example: 5/3 = 1/3 + 1/3 + 1/3 + 1/3 + 1/3 or 5 x 1/3 or (5 x 1)/3.

Multiply a whole number times any fraction less than 1 and justify the product.

Example: 5 x 2/3 is 5 sets of two-thirds, which is ten-thirds. or 5 x 2/3 = 5 x (2 x 1/3) = (5 x 2) x 1/3 = 10 x 1/3 or 10/3.

Solve word problems involving multiplying a whole number times a fraction using a visual model and equation to represent the problem.

Teacher Vocabulary:

Whole number

Fraction

Non-unit fraction

Unit fraction

Fraction less than one

Fraction greater than one

Visual fraction model

Equation

Decompose

Recompose

Compose

Knowledge:

Students know:

Models or equations to represent multiplication situations.

The fraction a/b is equivalent to the unit fraction 1/b being iterated or "copied" the number of times indicated by the numerator, a.

Skills:

Students are able to:

Model and explain how a non-unit fraction can be expressed as multiplication.

Multiply a whole number times any fraction less than one.

Solve word problems involving a whole number times a fraction using a visual fraction model and equation to represent the problem.

Understanding:

Students understand that:

Previous work involving multiplication with whole numbers can be extended to fractions in showing multiplication as putting together equal-sized fractional groups.

Problem solving situations involving multiplication of a whole number times a fraction can be solved using a variety of strategies, models, and representations.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.4.16.1: Recognize fractions in their simplest forms.
M.4.16.2: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
M.4.16.3: Demonstrate an understanding of fractional parts.
M.4.16.4: Apply properties of operations as strategies to multiply and divide.
M.4.16.5: Recall basic multiplication facts.
M.4.16.6: Define multiple.
M.4.16.7: Compare two fractions with the same numerator or the same denominator by reasoning about their size.
M.4.16.8: Recognize that comparisons are valid only when the two fractions refer to the same whole.
M.4.16.9: Record results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
M.4.16.10: Name the first ten multiples of each one-digit natural number.
M.4.16.11: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
M.4.16.12: Solve simple fractions using multiplication strategies.
M.4.16.13: Recognize equivalent forms of fractions.
M.4.16.14: Multiply proper fractions with common denominators 2-10.
M.4.16.15: Solve word problems using whole numbers.
M.4.16.16: Write number sentences for word problems.
M.4.16.17: Identify key terms in word problems.
M.4.16.18: Multiply and divide within 100.
M.4.16.19: Recall basic multiplication facts.

Prior Knowledge Skills:

Define fraction, numerator, and denominator.

Identify the parts of a fraction a/b as the quantity formed by a parts and size 1/b.

Label numerator, denominator, and fraction bar.

Identify parts of a whole with two, three, or four equal parts.

Distinguish between equal and non-qual parts.

Partition circles and rectangles into two and four equal shares; describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.

Demonstrate conceptual understanding of adding or subtracting 10 using concrete models.

Recognize the place value of ones, tens and hundreds.

Count forward and backward by 100.

Count forward and backward by 10.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.4.15 Model decomposing fractions having like denominators, using visual fraction models (limit to half and fourths).

16. Apply and extend previous understandings of multiplication to multiply a whole number times a fraction. Model and explain how a non-unit fraction can be represented by a whole number times the unit fraction. Example: 9/8=9 ×1/8 Extend previous understanding of multiplication to multiply a whole number times any fraction less than one. Example: 4 ×2/(3 )= (4 × 2)/3= 8/3 Solve word problems involving multiplying a whole number times a fraction using visual fraction models and equations to represent the problem. Examples: 3 × 1/2, 6 × 1/8