Students will explore modelling and solving one-step algebraic equations involving multiplication.

The purpose of the Day 4 activities is to reinforce key concepts from Day 3. 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.

• There are two types of division;
• Quotative division is when the total quota is known (the dividend), and the number per group or the rate (the divisor) is known;
• Quotative division reveals the number of copies or iterations of a rate that can be derived from the overall quota (the dividend);
• In quotative division, the dividend and the divisor have the same unit;
• The dividend from any division sentence can be decomposed into smaller parts to allow for friendlier division by the divisor. This strategy is known as partial quotients. (i.e.: 85 ÷ 5 = 45 ÷ 5 + 40 ÷ 5 = 9 + 8 = 17);
• Division is the inverse operation of multiplication;
• Variables are used to represent changing or unknown quantities;
• When solving an equation where the coefficient of the unknown variable is not equal to 1, division is required to determine the value of the unknown variable and the context of the problem determines which type of division is required.

Present the following multiplication and division equations one at a time. Encourage students to describe a quotative context that could be represented by each of the division sentences such as kilograms of bird seed (dividend) and kilograms per feeder (divisor) like we did in the last lesson. Students should use a model of their choice to solve and/or represent their thinking.

108 ÷ 9 = p

p(9) = 108

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Show the following visual math talk prompt and be ready to pause the video once prompted:

In the video, students are presented with the following context:

108 candies are divided into bags with 9 candies in each bag.

How many bags can we fill?

Although students are free to leverage the strategy and mathematical model of their choice, we are hoping to elicit the use of the open array or area model to demonstrate partial products and/or partial quotients.

In the visual example, we can see that the dividend was decomposed into 90 and 18 to more easily come to the result for our quotient.

Taking the “parts” and re-composing them, we have revealed the number of bags that we can create with 9 candies per bag.

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Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

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