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This is a fun quick way to practice or solidify concepts with students. I especially like this on days the schedule is shortened and I dont have time for a new lesson, or if my class is struggling with a specific concept. I also love it for review.
National Council of Teachers of Mathematics *
Try these online interactive manipulatives
try this if you want your students hands on
Need ways to create more practice on a specific concept? Try Twinkl. Tons of free worksheets.
This guide is designed for K-8 educators to bridge the gap between educational research and classroom practice. It focuses on high-leverage practices that build deep conceptual understanding, procedural fluency, and mathematical reasoning.
The CRA sequence is an evidence-based instructional approach that helps students build a mental bridge between physical objects and abstract symbols.
Concrete: Students interact with physical manipulatives (e.g., base-ten blocks, counters, fraction tiles) to model a concept.
Representational (Semi-Concrete): Students use drawings, tallies, dots, or number lines to represent the physical objects.
Abstract: Students use numbers and mathematical symbols (e.g., $ +, -, \times, \div $) to solve problems.
Implementation Tip: Do not rush to the abstract. Ensure students can explain the "why" using a drawing before moving exclusively to equations.
Subitizing: Use "Quick Images" with dot cards to help students recognize quantities without counting.
Counting Collections: Provide students with various items to count, encouraging them to organize items in groups of 5 or 10.
Ten-Frames: Use ten-frames to anchor numbers to 5 and 10, which is critical for future addition and subtraction strategies.
Array Modeling: Use arrays to transition from additive thinking (repeated addition) to multiplicative thinking.
Area Models to Multiply: Use the area model for multi-digit multiplication and division to visualize partial products.
Area Model or partial quotients to Divide
Fraction Equivalence: Use fraction strips and number lines to show that 1/2 is the same "size" as 2/4, rather than just teaching the "multiply by 2" rule.
Ratio Tables: Use tables to help students see the constant relationship between two quantities.
Double Number Lines: Effective for visualizing percentages and unit rates.
Visualizing Equations: Use algebra tiles to model solving for 2 x + 3= 7, ensuring students understand that an equation is a balanced scale.
Fluency is more than speed; it is the combination of accuracy, efficiency, and flexibility.
Number Talks: 5–15 minute daily mental math discussions where students share different strategies for solving a single problem.
Fact Strategies over Rote Memorization: Teach "Near Doubles" (e.g., if 6 + 6 = 12 , then 6 + 7 = 13 ) or "Bridge to Ten" (e.g., 8 + 5 is 8 + 2 + 3 ).
Number Lines: Use open number lines to model addition, subtraction, and elapsed time.
Move away from "keyword" charts (e.g., "altogether means add"), which often fail in complex word problems.
Three-Read Strategy:
First Read: What is the story about? (Context)
Second Read: What are the quantities? (Data)
Third Read: What is the question we are solving? (Goal)
Notice and Wonder: Show a graph or image and ask, "What do you notice? What do you wonder?" before giving a prompt.
CGI (Cognitively Guided Instruction): Focus on the different types of word problem structures (Join, Separate, Compare, Part-Part-Whole).
Low-Floor, High-Ceiling Tasks: Use tasks that all students can access but that can be extended for high-flyers (e.g., "The answer is 24. What is the question?").
Small Group Instruction: Use data from formative assessments to pull groups for targeted "just-in-time" support rather than "just-in-case" remediation.
Scaffolding: Provide sentence stems for mathematical discourse (e.g., "I agree with [Name] because...", "I solved it differently by...").
Exit Tickets: 1–2 questions at the end of a lesson to gauge immediate understanding.
Hinge Questions: A multiple-choice question midway through a lesson where each wrong answer reveals a specific misconception.
Math Interviews: Sit with a student for 2 minutes and ask them to "think out loud" while solving a problem.
Physical Manipulatives
Base-ten blocks, Cuisenaire rods, Pattern blocks, Two-color counters, Rekenreks.
Virtual Manipulatives
Math Learning Center Apps, Polypad by Desmos, Geogebra.
Instructional Tools
Desmos Classroom, Khan Academy (for procedural practice), Zearn.
The "Equals" Sign: Many students think = means "the answer is." Teach it as "is the same as" or "balanced with." Show equations like 5 + 2 = 4 + 3 .
Multiplying Decimals: Students often think "multiplication always makes a number bigger." Use visual models to show 0.5 \times 0.5 = 0.25.
Fraction Size: Students may think 1/8 is larger than 1/2 because 8 is larger than 2. Use visual area models to correct this.
Vertical Alignment: Ensure that the language used in 2nd grade (e.g., "composing and decomposing") matches the language used in 5th grade.
Coherence: Help students see that a ratio in 6th grade is an extension of the fractions they learned in 3rd grade.
Standard Algorithms: Introduce standard algorithms only after students have mastered the conceptual models (e.g., partial products before the standard multiplication algorithm).
Display Student Work: Show multiple ways to solve the same problem on the walls.
Wait Time: Give at least 5–10 seconds of wait time after asking a question.
Mistakes as Opportunities: Highlight a "Favorite Mistake" anonymously to analyze where the thinking went wrong and what can be learned.
Math Journals: Have students write about their process, not just their answers.