Foundations of Mathematical Thinking · Junior Infants

Active learning ideas

Introduction to Polynomials: Monomials and Binomials

Active learning helps students grasp the structure of monomials and binomials because these forms rely on precise definitions and operations. Concrete manipulatives and sorting tasks make abstract symbols visible, reducing confusion between terms and operations.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Algebra - A.1.11

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 30 min · Small Groups

Card Sort: Monomials vs Binomials

Prepare cards with expressions such as 4x, 9, 2y + 5, 3a - b, and distractors like 2x * 3. Students in small groups sort into monomial or binomial piles, justify each choice, then share one tricky example with the class.

Differentiate between a monomial and a binomial.

Facilitation Tip

During Card Sort: Monomials vs Binomials, circulate to listen for students’ explanations and gently correct misidentifications by asking them to justify their grouping.

What to look for

Provide students with a list of algebraic expressions. Ask them to circle the monomials and put a square around the binomials. Then, for one binomial, have them identify its two terms.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Think-Pair-Share
• 25 min · Small Groups

Like Terms Matching Relay

Divide class into teams. Display two expressions on board; first student runs to simplify by combining like terms, tags next teammate. Include monomials and binomials. Debrief simplifications as whole class.

Explain how to combine like terms in polynomial addition and subtraction.

Facilitation Tip

For Like Terms Matching Relay, set a timer for each round so students practice speed and accuracy while collaborating.

What to look for

On a small card, ask students to write one example of a monomial and one example of a binomial. For their binomial, they should label each of its terms.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Think-Pair-Share
• 40 min · Pairs

Algebra Tiles Addition Stations

Set stations with tiles for x-squared, x, and units. Students model two binomials, combine matching tiles to add or subtract, record the result. Rotate every 10 minutes through four problems.

Construct an example of a binomial and identify its terms.

Facilitation Tip

At Algebra Tiles Addition Stations, model how to arrange tiles to represent expressions before students build their own solutions.

What to look for

Pose the question: 'If you have 3 apples and your friend gives you 2 more apples, how many apples do you have?' Relate this to combining like terms in algebra. Then ask, 'What if you have 3 apples and 2 oranges, can you combine them into one term? Why or why not?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 04

• Think-Pair-Share
• 20 min · Pairs

Build Your Own Binomial

Provide term cards (e.g., 2x, -3y, 5). Individually or in pairs, students select two to form binomials, then add another binomial and simplify. Share and verify as whole class.

Differentiate between a monomial and a binomial.

Facilitation Tip

Before Build Your Own Binomial, provide sample expressions without solutions so students self-check their work against the rules.

What to look for

Provide students with a list of algebraic expressions. Ask them to circle the monomials and put a square around the binomials. Then, for one binomial, have them identify its two terms.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach this topic by starting with physical models like tiles or colored blocks to show why like terms combine while unlike terms do not. Avoid rushing to symbolic manipulation; allow time for students to verbalize the rules in their own words. Research shows that students who manipulate concrete objects before abstract symbols retain understanding longer.

Successful learning looks like students accurately identifying monomials and binomials, explaining why terms combine or stay separate, and performing addition or subtraction with like terms. They should use precise vocabulary and justify their reasoning with examples or models.

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Watch Out for These Misconceptions

• During Card Sort: Monomials vs Binomials, watch for students who group expressions like 2x * y as binomials.

  Have these students review the operation signs in their sorted piles. Ask them to circle the signs in each expression and explain why multiplication creates one term, not two.

• During Like Terms Matching Relay, watch for students who combine unlike terms such as 2x + 3y = 5xy.

  Use the relay’s colored strips to visually separate terms. Ask students to place matching colors together and explain why the colors must match for terms to combine.

• During Algebra Tiles Addition Stations, watch for students who stack variable tiles and constant tiles together regardless of type.

  Have students rebuild their expressions while naming each tile’s role. Ask them to point to the tile that represents the variable and the one that represents the constant to reinforce the distinction.

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Methods used in this brief

• Think-Pair-Share