Manipulatives- Math Grade 6-9

learning skilLS

instructional strategy

Use concrete materials, images and representational models to solve math problems

academic skill

Grade 6 – 9

Multiplication and Division: proportions and fractions

Lesson Objective, Goal and Success Criteria

  1. Construct proportion puzzles by identifying given ratios and unknown values.
  2. Apply proportional reasoning skills to arrive at accurate solutions to proportional puzzles.
  • Understand the concept of proportions and recognize their relevance in real-life scenarios
  • Understand representations of fractions and ratios, using fraction tiles and pattern blocks, as tools for representing
  1. Accurately represent proportions using pattern blocks
  2. Solve proportional puzzles through visual representations

UDL Instruction

  1. Instruct students to use at least 10 of the pattern blocks to create the first letter of their name.
  2. Invite students to share their creations with the class.
  3. Discuss how they approached the task and the choices made in representing their initial
  4. Introduce the criteria that 1 hexagon is 1 whole. Model for students how to calculate the value of their initial as a fraction, decimal, using a ratio.
  5. The teacher will introduce the concept of proportion puzzles using visual aids such as fraction tiles and pattern blocks to represent ratios and unknown values. A common misconception to anticipate is students confuse proportionality with equality. This will be addressed through visual and hands-on activities.

Differentiated Instruction

  • Working in pairs, students will solve a puzzle provided by the teacher. 
  • Each pair will be given a puzzle based on their ability. The students are expected to work together to figure out the solution to the puzzle. This type of activity promotes teamwork, problem-solving, and can be a fun and engaging way for students to apply their knowledge or skills in a practical context

  • Bring the students back together to discuss the reflection question: 
  • How did you know what the missing blocks were? Have students discuss in a small group and then invite volunteers to share with the whole class.

Measurement of Success

Students will participate in a quick closing activity where they will share their understanding of how proportion puzzles can be applied to real-life situations using Knowledgehook.

Materials, References and Resources

Chang, S. H., Lee, N. H., & Koay, P. L. (2017). Teaching and learning with concrete-pictorial-abstract sequence: A proposed model.

Hinton, V. M., & Flores, M. M. (2019). The effects of the concrete-representational-abstract sequence for students at risk for mathematics failure. Journal of Behavioral Education, 28(4), 493-516.

Hughes, E. M., Riccomini, P. J., & Witzel, B. (2018). Using concrete-representational-abstract sequence to teach fractions to middle school students with mathematics difficulties. Journal of Evidence-Based Practices for Schools, 16(2), 171-190.

Using the CRA Approach

The Best Hands on Fraction Activity Ever

Teaching Fractions Using Manipulatives


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