Learning Activity

Witches Brew With Fractions

Subject Area

Mathematics

Grade(s)

5

Overview

Students will be creating a Halloween-themed recipe and then altering it to feed various amounts of "witches". The students will practice both multiplying and dividing fractions.

This activity results from the ALEX Resource Development Summit.

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.

Unpacked Content

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.
Mathematics (2019) Grade(s): 5

MA19.5.14

Model and solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models, drawings, or equations to represent the problem.

Unpacked Content

UP:MA19.5.14

Vocabulary

  • Fraction
  • Models
  • Mixed number
  • Multiplication

Knowledge

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.

Skills

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.

Understanding

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.
Mathematics (2019) Grade(s): 5

MA19.5.15

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Unpacked Content

UP:MA19.5.15

Vocabulary

  • Unit fraction
  • Whole number
  • Division
  • Dividend
  • Divisor
  • Quotient
  • Equation
  • Multiplication
  • Factor
  • Fraction models

Knowledge

Students know:
  • Contextual situations involving division with whole numbers and unit fractions.
  • Strategies for representing a division problem with a visual model.

Skills

Students are able to:
  • Use previous understandings of operations to
  • Divide unit fractions by a whole number and whole numbers by unit fractions.
  • Use visual models to illustrate quotients.
  • Create story contexts for division.
  • Use the relationship between multiplication and division to explain quotients.

Understanding

Students understand that:
  • A variety of contextual situations are represented with division of a whole number by a fraction or a fraction by a whole number.
  • Quotients resulting from division of a whole number by a fraction or a fraction by a whole number can be illustrated and justified with a visual model.
  • The relationship between multiplication and division can be used to justify quotients resulting from division of a whole number by a fraction or a fraction by a whole number.

Phase

During/Explore/Explain
After/Explain/Elaborate
Learning Objectives

Learning Objectives

Students will be able to solve real-world problems involving multiplying and dividing fractions by a whole number by using visual models and equations.

Activity Details

Give each student a blank index card. Explain that they get to create a "Witches' Brew" using whatever disgusting ingredients they can imagine (fingernails, wolf hearts, eyeball juice, etc.). Their recipe will be enough to feed four witches. They must follow the guidelines:

    • You must use at least eight ingredients.
    • Each ingredient must be represented as a fractional amount.

After the students have created their recipe, they must figure out how much of each ingredient would be needed to make a brew to feed 12 witches (multiply amounts by three) and only one witch (divide amounts by four). A clever story keeps the students engaged -- for example, you might need a larger batch of the Brew because you're attending a broom convention, or you might need the one-serving version because your witch cousin is trapped inside a crystal ball and eats every meal alone.

The students should show the work of their calculations on paper. They can use models or equations, whichever they are more comfortable with.

If students finish early, they can draw a cauldron filled with their brew, including a visual representation of the correct amount of each ingredient.  

NOTE: Make sure students are going back to the original recipe amounts to perform their calculations.

In closing, ask questions such as:

  • Was it easier to multiply or divide the recipe?
  • How could we find the calculations using different operations?
  • How might this activity prepare you for the real world?
Assessment Strategies

Assessment Strategies

Assess students' final product to ensure they multiplied and divided fractions by a whole number correctly.

Variation Tips

Students can work with partners or in groups based on ability.  For a challenge, have students calculate the recipe for an odd number of witches, such as 18 (students will have to multiply by a fraction or break the calculation into parts).

Background and Preparation

Background / Preparation

Gather index cards, one per student.  If students are illustrating, they will need white paper and coloring materials.

Approved Date

Owner (Author)

seasley
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