Students will demonstrate the concepts and skills that they have developed through this context and learning experience.

The purpose of this assessment is for students to demonstrate their understanding of the following big ideas.

• Partitive division is one of the two types of division;
• When dividing partitively, the dividend and the divisor often (not always) have two distinct units;
• The resulting quotient has a compound unit (quantity of dividend per one unit of divisor);
• The dividend and the divisor are a ratio before the division is performed;
• The quotient is a rate;
• The quotient can be revealed through scaling the ratio in tandem to one whole of the divisor;
• There are two ways to half a fraction:
  • Half the numerator in order to half the number of parts while leaving the size of each part untouched (i.e.: half of \(\frac{4}{6}\) is \(\frac{2}{6}\)); or,
  • Double the denominator. Double the number of parts that make up the whole by partitioning the existing parts in half, and keep the number of parts (the numerator) the same (i.e.: half of \(\frac{4}{6}\) is \(\frac{4}{12}\)).

The independent assessment will allow students to demonstrate concepts and skills related to the following learning goals:

• I will divide fractions.
• I will represent a division sentence involving fractions through a context and a model.
• I will use a fraction as an operator to scale quantities.
• I will demonstrate an understanding of ratios and rates.
• I will demonstrate an understanding of the relationship between ratios, rates and partitive division.

Students might write and/or model their answers independently. Students can also be interviewed by their teacher.

An alternative assessment opportunity should be offered if this tool will not successfully capture what the student knows, understands or can do.

Present each division sentence one at a time. Encourage students to construct a context and model that could be represented by each sentence. Solve.

\(\frac{4}{5}\) ÷ \(\frac{2}{5}\)

\(\frac{6}{7}\) ÷ \(\frac{3}{4}\)

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Question #1:

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Question #2:

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Question #3:

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Question #4:

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Question #5:

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Based on the student thinking demonstrated on this assessment, provide students with descriptive feedback – written, verbal, or both – which includes next steps students should take in order to promote extending what they know, understand and can do.

Since assessment should be an opportunity for students to learn and for the teacher to understand where a student is in their learning journey, this should not close the door on these big ideas, models, and strategies.

What opportunities can you provide students with to demonstrate any further learning they engage in after this assessment day?

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