C2.1 · Add and subtract first-degree monomials using models

Ontario Grade 7 Mathematics

Algebra

Use variable tiles to show what each term means.

What you will learn

• Represent first-degree monomials with variable tiles.
• Use tile models to add and subtract matching monomials.
• Use a model to show when different tile groups must stay separate.

1. Read a tile model

• One x-tile represents x; several x-tiles represent a count of x.
• The number tells how many tiles, and the variable tells their label.
• Different variable labels mean different tile types.

2. Add matching tile groups

• Put matching tile groups together and count their tiles.
• Keep the same variable label in the result.
• Keep groups with different labels separate.

3. Subtract by taking tiles away

• Start with the first tile group.
• Remove the requested number of tiles with the matching label.
• Count what remains and keep its label.

4. Use the model to check your symbols

• Use the tile labels to decide whether groups match.
• Count tiles only after checking their labels.
• Read the result back as a tile model.

Worked example

Add x-tiles

1. Show the first group
   Place three x-tiles in a group. This is the tile model for the first term.
   $$3x=x+x+x$$
2. Add the next group
   Place four more x-tiles with the first group. Every tile has the same label, so count all the tiles together.
   $$3+4=7$$
3. Record the model
   There are seven x-tiles. Write seven with the same x label.
   $$3x+4x=7x$$

Worked example

Subtract y-tiles

1. Set out the starting group
   Place nine y-tiles. The first term names the starting group.
   $$9y=y+y+y+y+y+y+y+y+y$$
2. Take away tiles
   Remove five y-tiles. Their labels match the starting tiles, so these are the tiles named by the subtraction.
   $$9-5=4$$
3. Record what remains
   Four y-tiles remain. Keep the y label because every remaining tile is a y-tile.
   $$9y-5y=4y$$

Worked example

Keep different tile groups separate

1. Build the two groups
   Make one group of three x-tiles and another group of two y-tiles. The labels show that the groups are different kinds.
   $$3x=x+x+x$$
2. Check the labels
   The model has three x-tiles and two y-tiles. Since the labels do not match, keep the groups separate rather than counting them as one kind of tile.
   $$3x+2y$$
3. Describe the result
   There are five tiles in total, but they are not five matching tiles. Keep both groups in the expression.
   $$3x+2y$$

Common mistakes and how to avoid them

Lesson summary

• A variable tile stands for one amount with a named label.
• Matching tiles have the same variable label.
• For addition, put matching groups together and count the tiles.
• For subtraction, remove matching tiles and count what remains.
• Keep different tile labels in separate groups.

Check your understanding

Key terms

Variable

A letter that stands for a number.

Term

One part of a mathematical expression, such as 3x.

Monomial

A single term, such as 3x or 4y.

First-degree monomial

A single term with a variable to the first power, such as x or 3x.

Matching tiles

Tiles with the same variable label.

Continue through Grade 7 Math

View the complete Grade 7 Math Ontario Grade 7 Mathematics curriculum and lessons

• C1.3 · Extend patterns and use their rules to find missing values
• C2.2 · Evaluate expressions with whole numbers and decimals
• C1.1 · Compare repeating, growing, and shrinking patterns by rate and starting value
• C1.2 · Represent number patterns with tables, expressions, and linear equations
• C2.3 · Solve and verify multi-term equations with whole numbers and decimals
• C3.1 · Write efficient code using counts, subprograms, and control structures

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 7 Mathematics, expectation C2.1. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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