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The Guides for Effective Instruction in Mathematics Revised

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C2.1 Add monomials with a degree of 1 that involve whole numbers, using tools.

Activity 1: Area and Addition of Monomials

Materials

  • colour tiles or virtual tiles
A box of tiles for handling material.

Have students represent a polygon with colour tiles using only one colour of tile. Ask them to choose a monomial of degree 1 to represent the area of one tile.

Afterwards, have students express the area of their polygon as an algebraic expression in two different ways (adding the monomials).

Have half of the students circulate around the classroom and observe the other students' polygons. Ask them to check whether the two algebraic expressions represent the area of the polygon constructed. Then alternate by having the other half of the students circulate around the classroom and observe the other students' work.

Example

Figure one: polygon shaped as “h” capital letter. It is created with 18 squares. Figure 2: polygon shaped as “h” capital letter. It is created with 18 squares. The group of 6 squares are circled.Figure 3: polygon shaped as “h” capital letter. It is created with 18 squares. 4 groups of 2 and one group of ten are circled.

Activity 2: Addition of Monomials With a Degree of 1

Present students with the following scenario:

Maëlie has 5 packages of apples, while Loïc has 3. How many apples do they have in total? Write an algebraic expression that represents this situation and solve the problem.

Strategy 1: Calculations Using Repeated Addition

I wrote 5x +3x, as an algebraic expression, where x is the quantity of apples.

To solve the expression, I can do a repeated addition.

5 “x” plus 3 “x” equal “x” plus, “x” plus, “x” plus, “x” plus, “x” “plus”, “x” plus “x” plus “x” equal 8 “x”

Strategy 2 : Calculations Using an Algebraic Expression (or a Symbolic Representation)

5x + 3x

I group like terms together to simplify the expression.

(5 + 3)x = 8x

Strategy 3: Calculations Using a Concrete or Visual Representation

I can group all like terms together.

Block of “x”

So:

8 blocks of “x” 5 “x” plus 3 “x” equal 8 “x”

Activity 3: Addition of Monomials

Ask students to add the following monomials:

  1. x + y + 2x + 3

Strategy 1

Representing Addition With Words

x + y + 2x + 3

1 group of x + 2 groups of x = 3 groups of x

1 group of y

The number 3

So I get 3 groups of x + 1 group of y + 3

3x + y + 3

Strategy 2

Representing Addition Using Algebraic Expressions

“x” plus “y” plus 2 “x” plus 3 equal one “x” plus one “Y” plus 2 “x” plus 3.Equal, open parenthesis, one plus 2, closed parenthesis, “x” plus one “y” plus 3.Equal 3 “x” plus, one “y” plus 3

Strategy 3

Representing Addition Using Concrete or Visual Representation

1st line: block “x”, block “y”, block “x”, square marked 1.2nd line: block “x” and square marked 1.3rd line: square marked 1.

I can group like terms together.

1st line: one block “x”, one block “y”, and one square marked one.2nd line: block “x” and one square marked one. 3rd line: block “x” and one square marked one.
  1. b) 3x +7y +6x + y

Strategy 1

Representing Addition Using Algebraic Expressions

I can only add like terms.

I group like terms together.

Open parenthesis 3 “x”, plus 6 “x”, closed parenthesis, equal, open parenthesis 7 “y”, plus “y”, closed parenthesis.

For each set of like terms, I add numbers in front of the variable.

Open parenthesis 3 “x”, plus 6 “x” closed parenthesis, equal, open parenthesis 7 “y”, plus “y”, closed parenthesis, equal 9 “x”, plus 8 “y”.

Strategy 2

Representing Addition Using Concrete or Visual Representation

Representation of concrete and visual. One column of 3 blue rlocks “x”, one column or 7 red blocks, one column of 6 blue blocks “x”, and one column of one red block “x”.

I can group like terms together.

Regrouping of similar terms. One column of 9 blue blocks “x” and column of 8 red blocks “y”.

Source : En avant, les maths!, 6e année, CM, Algèbre, p. 2-6.