ALEX Learning Activity

  

Fraction Equivalence: Happy by Design

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  This learning activity provided by:  
Author: Samantha Wallace
System:Limestone County
School:Cedar Hill Elementary School
  General Activity Information  
Activity ID: 2550
Title:
Fraction Equivalence: Happy by Design
Digital Tool/Resource:
Tenths & Hundredths Struggle Problem Slideshow
Web Address – URL:
Overview:

Students will work in groups to solve a task involving a 10x10 grid.  They will be asked to represent the same amount in both tenths and hundredths, making connections between equivalent fractions with 10 and 100 as the denominator.

 

This activity results from the ALEX Resource Development Summit.
  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 4
17. Express, model, and explain the equivalence between fractions with denominators of 10 and 100.

a. Use fraction equivalency to add two fractions with denominators of 10 and 100.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this technique to find the sum of two fractions with respective denominators 10 and 100.
Teacher Vocabulary:
  • Equivalence
  • Denominator
  • Fraction model
  • Tenths
  • Hundredths
  • Sum
Knowledge:
Students know:
  • Strategies for generating equivalent fractions.
  • Strategies for adding fractions with like denominators.
Skills:
Students are able to:
  • Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100.
  • Use models to illustrate equivalency between fractions with denominators of 10 and 100.
  • Explain equivalency between fractions with denominators of 10 and 100.
  • Use equivalency to add two fractions with denominators of 10 and 100.
Understanding:
Students understand that:
  • equivalent fractions are fractions that represent equal value.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.4.17.1: Recognize equivalent forms of fractions and decimals.
M.4.17.2: Demonstrate equivalent fractions using concrete objects or pictorial representation.
M.4.17.3: Recognize pictorial representations of equivalent fractions and decimals in tenths and hundredths.
M.4.17.4: Define equivalency.
M.4.17.5: Identify place value of decimals to the tenths and hundredths.
M.4.17.6: Use place value understanding to round whole numbers to the nearest 10 or 100.

Prior Knowledge Skills:
  • Define equivalent.
  • Recognize pictorial representations of equivalent fractions.
  • Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.
  • Recognize that equal shares of identical wholes need not have the same shape.
  • Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
  • Label a fraction with multiple representations.
  • Partition circles and rectangles into two and four equal shares; and describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.
  • Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.
  • Label a pictorial representation.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.17 Model equivalence between fractions of a whole, halves and fourths using visual models.
Learning Objectives:

Students will be able to create equivalent fractions with denominators of 10 and 100 using a model.
  Strategies, Preparations and Variations  
Phase:
Before/Engage
Activity:

  • Begin by telling the students that they will be working together to solve a problem.  If students are not sitting in groups, put them in groups of 3-4.

  • Display Slide 2 on the “Happy by Design” slideshow.  Read the problem aloud and give students time to look at the design.  Ask students if they can answer the problem -- if they immediately answer yes or no, ask them if they can justify their answer.

  • Display Slide 3.  Part A asks the students to figure out exactly how much of the figure is shaded -- they should count and realize there are 40 squares out of 100 that are shaded.  This might be enough to answer the question about Malik’s discount, but we can explain and justify our answer by representing the shaded amount as a fraction (40/100).  Malik does get the discount because 40/100 is less than half, which would be 50/100.

  • After students have discussed Part A, direct their attention to Part B.  How can we represent the shaded part in a different way besides 40/100?  Encourage students to think outside the box.  We’re looking for 4/10, but other answers may be correct also.

  • If students are struggling, ask them if we could rearrange the shaded squares.  Provide students with copies of a hundred-grid and encourage them to shade in 40 squares all together, instead of the design that Malik used.  It might be helpful to model this on a document camera if students need extra support.

  • Close the activity by emphasizing that Malik’s design had 40 squares out of 100 shaded in, which is 40/100 and also four columns out of 10 shaded in, which is 4/10.
Assessment Strategies:

Observe students and see if they are able to explain the equivalence between 40/100 and 4/10.  To get a quick check, write the fraction 20/100 on the board and ask students to create an equivalent fraction using 10 as the denominator.
Advanced Preparation:

You will need to have a projector and board to display the slideshow.

Have copies of blank hundred-grids available for students to use.
Variation Tips (optional):

Some students might need to see a grid that is only divided into tenths to make the connection between the rows/columns on the 10x10 grid.  As an extension, students can make a design on a 10x10 grid by shading in exactly 30 squares.  After making the design, ask them to represent the amount with two different equivalent fractions.
Notes or Recommendations (optional):

17. Express, model, and explain the equivalence between fractions with denominators of 10 and 100.
a. Use fraction equivalency to add two fractions with denominators of 10 and 100.
  Keywords and Search Tags  
Keywords and Search Tags: decimal, equivalent, fraction, hundredth, tenth