Fraction practice part 1

1. Equivalent fractions using a visual model. Explain how we know that 14/6 = 7/3.

Things I look for in an explanation:

• Use a visual model.
• The visual model should show that 14/6 and 7/3 are equivalent by either
  • showing they are two names for the same amount (ideally by regrouping within the same picture rather than by drawing two separate pictures, but if they are shown on separate pictures the wholes should be the same
  • or showing that they are two names for the same point on the number line.
• There should be an in-words explanation of the equivalence in words (using one of the above reasons)
• An accompanying numerical strategy should be shown (either multiplying numerator and denominator by the same number of dividing numerator and denominator by the same number).
• There should be an in-words explanation of how to see the numerical strategy in the visual model (should be explaned in terms of why it is multiplication or why it is division, which goes beyond demonstrating that the numerical answers are the same).

2. Multiplying fractions: Explain multiplication of fractions using a visual model for the two examples: 2/3 x 4/5 and 13/6 x 8/5

Things I look for in an explanation:

• Use a visual model
• Explain in words the rationale for the visual model (can be either fraction of a fraction or rectangular area).
  • Note: the visual model must match the explanation.
• The numerical strategy is shown
• There is an in-words explanation of how the numerical steps are shown in the diagram. This should include both:
  • How the numerator and the denominator values are shown in the diagram
  • How the products can be deduced from the diagram (what to multiply together and why).

Fraction practice part 2

3. Adding fractions: Explain addition of fractions using a visual model for the example 3/4 + 2/5

Things I look for in an explanation:

• Use a visual model, where both fractions are represented in terms of the same sized whole.
• Show on the model and explain in words the process of finding equivalent fractions with the same denominator.
• Show in numbers the process of finding equivalent fractions, and use the visual model to explain the numerical process (how can you see the products in the diagram or in the process of creating the diagram)
• Show with numbers the process of adding together the fractions with the same denominator. Explain in words why you add the numerators but the denominators stay the same.

4. Subtracting mixed numbers. Explain subtraction of mixed numbers for the example: 5 1/3 - 1 3/4. You should include in words explanations that would address or help to correct the common error that leads to the incorrect answer of 4 5/12

Things I look for in an explanation:

• An explanation in words of why you must convert all or part of the whole number 5 into a fraction
• An explanation in numbers and words of what you are doing to find equivalent fractions with the same denominator
• An explanation using numbers and words of what you are doing and why to find the final answer.

5. Dividing fractions: Explain division of fractions using a visual model for the example 7/4 ÷ 2/3

Things I look for in an explanation:

• A restatement of the problem using either a partitive or a measurement division context
• A visual representation of the problem that is robust enough that the calculations can be explained by the visual model alone.
• An explanation of how to deduce from the visual model that you should divide 7/4 by 2 and multiply it by 3 (in either order)
• An explanation that dividing by 2 and multiplying by 3 is the same as multiplying by 3/2.