C. Hodson (2018)
Grade 7 Number Sense and Numeration
– add and subtract fractions with simple like and unlike denominators, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, calculators) and algorithms;
– demonstrate, using concrete materials, the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number (e.g., ½ + ½ + ½ = 3 x ½ );
Grade 8 Number Sense and Numeration
– represent the multiplication and division of fractions, using a variety of tools and strategies (e.g., use an area model to represent ¼ multiplied by 1/3;
– solve problems involving addition, subtraction, multiplication, and division with simple fractions;
I like to use measuring cups (and cooking or baking) to demonstrate and assess understanding of fractions. Fraction circles, strips and rods are used at earlier grades and also have their place in the intermediate classroom. However, for students who have already decided they don’t like math or for those who are disengaged/disinterested, I like to incorporate baking as much as possible. It’s less stressful for me to bake with intermediate students; they don’t require the same supervision to use the oven or other cooking tools.
I begin by introducing measuring cups and sand. How can we get 1 cup when we don’t have a 1 cup measure? How can we get 4 cups when we don’t have a four cup measure? Bringing the sand table from kindergarten sparks some interest and invites students to play. I increase the complexity of the question as students become more comfortable.
Baking is a great way to test conceptual knowledge of fractions too. I can differentiate my assessment by giving different tools to each group. For students who are in the concrete stage, I give the exact measuring cups they need. 1/4, 1/3, 1/2, and 1. They still need to demonstrate that 3/4 equals ¼ + ¼ + ¼ and that ½ = ¼
For groups who have mastered this, I give mismatched measuring cups. For example, if they need 1/3 of a cup of one ingredient, I might give them a set of cups that is missing the 1/3 cup measure. How will they measure 1/3 cup? Or I might only provide 1/3, 2/3 and 3/4 cup measures when they need 3 cups of something. What’s the easiest way to measure 3 cups? How can they measure 3 cups with the fewest movements?
For students who truly understand how adding and multiplying fractions work, I ask them to double or triple the recipe, and write the recipe out for me before we start baking.
I did this with four groups, all differentiated in some way, but all baking the same recipe. The proof is in the pudding…or in this case it was in the cookies. How did they look? Taste? What did we learn? What would we do differently?
You do have to be willing to risk some failures, but students are highly motivated when they get to eat their work. They are also more willing to look at their mistakes when they don’t taste right (especially if we are planning to bake again soon).
Using measuring cups helps to move students from concrete to more abstract thinking because they help students to see the relevant use of fractions. They are different than the manipulatives typically used – fraction strips, circles, rods, etc. Using a different manipulative reinforces concepts that have already been attained, but for those who were not successful may provide another opportunity to learn. Measuring 1/3 of a cup three times and filling the 1 cup measure with sand highlights that 3 x 1/3 is the same as 1 whole.
(Always double check that your measuring cups are measuring what you think they are. Is your 1/3 cup accurate? Will 3 of them actually give you 1 cup when you measure it out. Sometimes the measuring cups from the Dollar Store are off a bit. You may also have to teach how to use dry measuring cups – level the top.)
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