Exploring Improper Fractions With Pattern Blocks

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

5

Overview

This activity is an exploration of mixed numbers, improper fractions, multiplying fractions by a whole number, and adding fractions with unlike denominators. The students will create a digital design using virtual pattern blocks. Counting the hexagon as one whole, the students will multiply the fractional pieces of their design and then use a blank pattern block template to add fractions with unlike denominators and find the total value for the picture.

This activity results from the ALEX Resource Development Summit.

Phase

Before/Engage
During/Explore/Explain
Mathematics (2019) Grade(s): 5

MA19.5.10

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.

UP:MA19.5.10

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.
Mathematics (2019) Grade(s): 5

MA19.5.12

Apply and extend previous understandings of multiplication to find the product of a fraction times a whole number or a fraction times a fraction.

UP:MA19.5.12

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.
    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.

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.

Learning Objectives

Students will be able to use models to represent improper fractions and mixed numbers.

Students will be able to add fractions with unlike denominators using a visual model.

Students will be able to multiply fractions by a whole number using visual models.

Activity Details

The students will explore fractions by creating pictures using pattern blocks. This is an exploration activity to set the stage for explicit instruction on converting improper fractions to mixed numbers, adding fractions with unlike denominators, and multiplying fractions by a whole number.

  • Explain that the students are going to create a design to help learn about fractions.
  • Show the pattern block tool on the board and explain how to manipulate the pieces (place/remove, rotate, etc.). Explain that the yellow hexagon is “one whole” and lead the students to figure out the fractional amounts for the other pieces. The students should see that it takes three blue pieces to make one yellow piece, so each one represents â…“. The red trapezoid is ½, the blue rhombus is â…“, and the green triangle is â…™.
  • The students should record the values for each shape in their journals.
  • Ask several turn-and-talk questions to build the foundation of the pieces as fractions, such as:
    • If you wanted to show the fraction â…”, what pieces would you need?
    • Which is greater, 2 green pieces or 1 red piece?
    • How many different ways could you show the amount 3/6?
  • Explain that the students are going to be building a design using the pattern block pieces. They can use only the yellow, red, blue, and green pieces (the others aren’t exact fractional amounts). There are templates available with the digital tool if the students are struggling with creativity.
  • After the students have finished building their design, they should record the quantity of each shape used in their journals (6 hexagons, 14 trapezoids, etc.).
  • Show an example design (a flower is easy to make) and model how to calculate the total for the entire design.  A blank pattern block template is helpful -- the teacher can provide these for the students to use as a resource during the calculations.  The students combine the pieces of their design by shading in sections of the blank shapes on the template. Students should count the total number of “wholes” they were able to make to get the total value for the design.
  • Students should record their totals as both an improper fraction and a mixed number in their journal.  For example: 14 green triangles = 14/6 = 2 2/6.  Students can then use the blank template to combine all of the values together to find the total value for the picture.
  • After students have finished calculating their totals, ask a few questions to debrief and check student understanding:
    • How many thirds does it take to make one whole? What happens if you use more than three?
    • How do we add together pieces of different sizes, like ½ and â…™? (Lead the students to see that we have to compare them to a common shape. This sets the stage for finding common denominators.)

Assessment Strategies

Observe to see if students are able to correctly shade in the blank shapes on the pattern block tool sheet. Check for any gaps in understanding related to comparing pieces of different sizes or in modeling fractions greater than one whole. Also, check to make sure that the total sum of the design is a reasonable answer.

Variation Tips

  • Consider continuing the debriefing discussion to explicitly teach converting improper fractions and mixed numbers, finding the common denominator, or writing the equations for multiplying fractions.
  • If students need more direct instruction, consider having everyone build the same design and calculate the totals for the picture together (guided practice).
  • For enrichment, give students a total (ex: 24 â…“ ) and have them work to make a design that meets the total. An extra challenge would be to include restrictions or requirements: at least 16 green triangles, an odd number of red trapezoids, no more than 5 yellow hexagons, etc.

Background / Preparation

Prepare copies of the blank pattern block tool sheets for the students to use as a resource during the calculating section of the lesson. You may wish to laminate these and have the students use dry erase markers so they can be reused in further lessons or in centers.

Make a sample design using the pattern block tool to use for modeling the procedure.

https://apps.mathlearningcenter.org/pattern-shapes/

Approved Date

Owner (Author)

seasley
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