Students will continue developing their ability to represent fractions for the purpose of adding.

The purpose of the Day 4 activities is to reinforce key concepts from the previous lessons in this unit. Students will engage in a string of related problems through a math talk and will have an opportunity to complete independent purposeful practice.

The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas.

• Fractions can be represented in a variety of ways;
• How you partition the whole determines the fractional unit (i.e.: partitioning a whole into 6 parts will result in 6 sixth parts);
• As you partition a whole into more parts, the smaller the size of each part;
• As you partition a whole into more parts, the larger the unit fraction (called the denominator in later grades);
• In order to compare two or more fractional quantities, the whole must be the same;
• The count (called the numerator in later grades) indicates the number of parts relative to the number of parts in the whole indicated by the unit fraction (the denominator);
• Fractional amounts exist between whole numbers;
• Different unit fractions can be used to represent equivalent quantities; and,
• The commutative and associative properties of addition (this big idea may emerge through student strategies)

Ask students to reason through the following addition sentences.

It might be helpful to share a context that will serve to emerge the number line or bar model as a tool.

For example, leveraging the context of the Wooly Worm Race could be helpful using a story similar to:

During off-season training, Yo Gabba Gabba practiced for a “two-heat” competition where the total distance of two races are measured to determine the winner. Here are the results measured for Yo Gabba Gabba. What was his total distance in each set of two-heats?

1 fourth + 2 fourths
1 third + 1 third
2 fifths + 2 fifths

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Question #1:

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Question #2:

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Question #3:

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Based on the student thinking demonstrated on this purposeful practice, provide students with descriptive feedback – written, verbal, or both – which includes next steps students should take prior to engaging in the assessment provided in the next lesson.

We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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