Big Idea:

Variables and Equations

Expectations:

C. Algebra

C2. Equations and Inequalities: demonstrate an understanding of variables, expressions, equalities, and inequalities, and apply this understanding in various contexts

Variables: C2.1 describe how variables are used, and use them in various contexts as appropriate

Equalities and Inequalities: C2.2 determine whether given sets of addition, subtraction, multiplication, and division expressions are equivalent or not

Equalities and Inequalities: C2.3 identify and use equivalent relationships for whole numbers up to 1000, in various contexts

teacher background

Students may benefit from prior experience with:

• adding and subtracting two-digit numbers

• modelling and describing equality as balance

• determining the unknown in addition and subtraction equations

KEY CONCEPTS:

• Variables are used in formulas (e.g., the perimeter of a square can be determined by four times its side length (s), which can be expressed as 4s).

• Variables are used in coding so that the code can be run more than once with different numbers.

• Variables are defined when doing a mathematical modelling task.

Note

• Identifying quantities in real life that stay the same and those that can change will help students understand the concept of variability.

• Identifying what is constant and what changes is one aspect of mathematical modelling.

• When students find different addends for a sum no more than 200, they are implicitly working with variables. These numbers are like variables that can change (e.g., in coding, a student’s code could be TotalSteps = FirstSteps + SecondSteps).

• In mathematics notation, variables are only expressed as letters or symbols. When coding, variables may be represented as words, abbreviated words, symbols, or letters.

• Students are also implicitly working with variables as they are working with attributes (e.g., length, mass, colour, number of buttons), as the value of those attributes can vary.

LOOK-FORS:

• Are students able to use the associative property to make addition equations easier to solve?

• How do students decide how to decompose a number (e.g., do they look at the ones digit and decide how many more ones are needed to make 10)?

• Do students realize that there is more than one way to decompose numbers to make addition easier?

• Once students have decomposed a number, how do they find the sum (e.g., using a number line, using mental math, adding tens and then adding ones)?

Have students share and model the strategies they used to add. Show each strategy on an open number line.

Discuss how students decided how to decompose a number. Did they look at the ones digit and find how many more ones were needed to make a friendly number (e.g., 27 + 44: 27 + __ = 30; I need to add 3 more ones to 27 to make 30, so decompose 44 into 3 and 41)?

Help students see that there is more than one way to decompose the numbers (e.g., 27 + 44: I need to add 6 more ones to 44 to make 50, so decompose 27 into 6 and 21).

Discuss how using the associative property can make addition and subtraction easier.

To allow students to show what they have learned in this lesson, go to the Exit Ticket and/or Practice.

Highlight for Students

• We can decompose numbers to make addition and subtraction easier; for example, 28 + 34 = 28 + 2 + 32.

• The associative property tells us that the numbers being added can be grouped without changing the sum.

Accommodation: Provide smaller measures for students to work with (e.g., lengths for 1-year-old baby: tip of finger to wrist: 7 cm; wrist to shoulder: 18 cm). Encourage students to use counters or linking cubes and a pan balance to help.

Extension: Have students find their height by adding the lengths of parts of their body (e.g., from floor to knee, then from knee to waist, and then from waist to top of head).

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