Teacher Resources

What the Research Recommends

Provide systematic instruction during intervention to develop student understanding of mathematical ideas. Build knowledge incrementally, break complex skills into manageable steps, model new ideas with clear think-alouds, and move from guided practice to independent practice with cumulative review.

Why It Matters

Students who struggle in math rarely fill gaps on their own. A deliberate sequence — like terms first, then the distributive property, then deciding whether two expressions are equivalent — keeps every new idea connected to something students already understand.

What It Looks Like in the Classroom

Suggested classroom applications for 6.EE.3 and 6.EE.4 — not part of the WWC recommendation itself.

• Teach equivalent expressions in a planned order: combine like terms (3x + 2x), then distribute (3(x + 2)), then compare forms.
• Model each new skill with a think-aloud before asking students to try it.
• Mix earlier skills into every practice set so nothing is forgotten.

Questions to Ask Students

• What is the first step, and why?
• How is this problem like the one we solved yesterday?
• How do you know these two expressions are equivalent?

What the Research Recommends

Teach clear and concise mathematical language and support students' use of the language to help them effectively communicate their understanding of mathematical concepts.

Why It Matters

Vague words hide vague thinking. When a student can say "the coefficient 3 means three groups of x" instead of "you times it," you can hear exactly what they understand — and what they don't.

What It Looks Like in the Classroom

Suggested classroom applications for 6.EE.3 and 6.EE.4 — not part of the WWC recommendation itself.

• Introduce and revisit precise terms: term, coefficient, like terms, equivalent, distribute.
• Ask students to explain why 2(x + 3) = 2x + 6 using the vocabulary, not just the steps.
• Keep a small word wall of expression terms students can point to while they talk.

Questions to Ask Students

• What makes two terms "like terms"?
• What does the coefficient tell you?
• Use the word "equivalent" in a sentence about these expressions.

What the Research Recommends

Use a well-chosen set of concrete and semi-concrete representations to support students' learning of mathematical concepts and procedures.

Why It Matters

The distributive property stops being a rule to memorize when students can see it. Three groups of (x + 2) tiles visibly contain three x-tiles and six unit tiles — that is 3x + 6, and the equivalence is something students discover rather than accept.

What It Looks Like in the Classroom

Suggested classroom applications for 6.EE.3 and 6.EE.4 — not part of the WWC recommendation itself.

• Build 3(x + 2) as three groups of x + 2 tiles, then count the tiles to reach 3x + 6.
• Have students draw their tile arrangements as a bridge from concrete to symbolic.
• Use tiles to test whether two expressions are equivalent before proving it with symbols.

Questions to Ask Students

• What does each tile stand for?
• Show me the 3 groups. Where do the 6 units come from?
• Can you build both expressions? Do they use the same tiles?

What the Research Recommends

Use the number line to facilitate the learning of mathematical concepts and procedures, build understanding of grade-level material, and prepare students for advanced mathematics.

Why It Matters

A number line turns "equivalent" into something testable: if two expressions always land on the same point, they are the same quantity. That idea — same value for every value of x — is the heart of 6.EE.4.

What It Looks Like in the Classroom

Suggested classroom applications for 6.EE.3 and 6.EE.4 — not part of the WWC recommendation itself.

• Plot x + x and 2x for several values of x and show they always land on the same point.
• Use the line to compare 3x + 2 and 3(x + 2) and see where — and why — they differ.
• Connect jumps on the number line to repeated addition and to coefficients.

Questions to Ask Students

• Where would 2x land when x is 4? Where would x + x land?
• If two expressions always land on the same point, what does that tell us?
• Find a value of x where these two expressions land on different points.

What the Research Recommends

Provide deliberate instruction on word problems to deepen students' mathematical understanding and support their capacity to apply mathematical ideas.

Why It Matters

Students who hunt for keywords write 3x + 2 when the situation calls for 3(x + 2). Teaching the underlying structure — groups, totals, and what the variable stands for — is what lets expressions mean something.

What It Looks Like in the Classroom

Suggested classroom applications for 6.EE.3 and 6.EE.4 — not part of the WWC recommendation itself.

• Pose situations like "3 friends each get x stickers plus 2 extras" and compare 3(x + 2) with 3x + 2.
• Ask students to write an expression first, then a story that matches it.
• Have students explain what each part of their expression represents in the story.

Questions to Ask Students

• What does x stand for in this problem?
• Does the 2 get multiplied by 3? How do you know?
• Write a story that matches 4(x + 5).

What the Research Recommends

Regularly include timed activities as one way to build fluency in mathematics, so students retrieve basic facts and critical steps quickly and accurately.

Why It Matters

When identifying like terms or recalling facts is automatic, students have mental room left for the real thinking — deciding whether two expressions are equivalent. Fluency practice supports the standard; it never replaces understanding.

What It Looks Like in the Classroom

Suggested classroom applications for 6.EE.3 and 6.EE.4 — not part of the WWC recommendation itself.

• Run brief, low-stakes timed rounds: sort terms into like-term pairs, or match equivalent expressions.
• Track growth against each student's own previous score, not against classmates.
• Keep timed work short and follow it with untimed reasoning problems.

Questions to Ask Students

• Which pair of terms can you combine fastest — and why those?
• What strategy helped you match equivalent expressions more quickly today?