ALEX Learning Activity

  

Multiply Fractions by Whole Numbers

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

You may save this Learning Activity to your hard drive as an .html file by selecting “File”,then “Save As” from your browser’s pull down menu. The file name extension must be .html.
  This learning activity provided by:  
Author: Ginger Boyd
System:Geneva County
School:Samson Middle School
  General Activity Information  
Activity ID: 2582
Title:
Multiply Fractions by Whole Numbers
Digital Tool/Resource:
Multiply Fractions by Whole Numbers
Web Address – URL:
Overview:

This learning activity is a free interactive fraction game from Math Games that will give students the opportunity to demonstrate their knowledge of multiplying a whole number by a fraction. Students will be asked a series of word problems involving multiplying a whole number by a fraction. Some questions will have multiple choice answers and some will require a free-response. There are four different levels of the game. Students advance each level based on the number of correct questions answered. This activity should be used at the end of a lesson on multiplying a whole number by a fraction to assess mastery of the standard.

This activity results from the ALEX Resource Development Summit.
  Associated Standards and Objectives  
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).
Learning Objectives:

Students will be able to:

    • model and explain a fraction as a multiple of a unit fraction.

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

    • solve word problems involving multiplying a whole number times a fraction using a visual model and equation to represent the problem. 
  Strategies, Preparations and Variations  
Phase:
After/Explain/Elaborate
Activity:

Students should have been introduced to multiplying a whole number by a fraction and have had an opportunity to explore and investigate the concept. The teacher may choose to review the multiplying a whole number by a fraction as an introduction to this learning activity. This activity can be used to give students the chance to demonstrate their knowledge of multiplying a whole number by a fraction.

The teacher should provide the students with a link to the website Multiply Fractions by Whole Numbers and explain directions for how to use the website. 

The students should have discovered in class that there are three simple steps to multiplying fractions by whole numbers: multiply tops, multiply bottoms, and simplify. During this activity, students will demonstrate how well they can apply those three simple steps to multiplying fractions by whole numbers to solve word problems.

Some questions will have multiple choice answers while others will require a free-response. There are four levels and students advance to each level based on correct answers.

As students explore the game, the teacher should walk around the room and observe any students who might be struggling to correctly apply the three simple steps when multiplying a fraction by a whole number.

The game also includes a built-in scratchpad for students to demonstrate their thinking.
Assessment Strategies:

The game itself can be used as an assessment. If playing the game as a whole group, the teacher can ask the students to answer each problem in their math journals and highlight the answer before giving the correct answer to the class.  

If playing the game individually, the teacher will want to circulate around the room to observe the class for struggling students.
Advanced Preparation:

Internet-connected devices will be needed to play the game. If the teacher wishes to play the game whole group, an interactive whiteboard and projector will also be needed.
Variation Tips (optional):

This game allows students to utilize a scratchpad to demonstrate their thinking. Students will click on the scratchpad and using the pencil icon, draw right over the word problem to solve the equation.

The game also allows students to have the word problem read to them for students who may struggle with reading.

This game could be used as a whole group activity or assigned as an individual activity. When using it whole group, teachers can allow students to answer in their math journals first, highlight the answers, then answer on the interactive whiteboard as a whole group.
Notes or Recommendations (optional):

ALCOS 2019

4.16). 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
  Keywords and Search Tags  
Keywords and Search Tags: compose, decompose, equation, fraction, nonunit fraction, unit fraction, whole number