1-Manipulatives- Math Proportions & Fractions Grade 6-9 (SAMPLE)

learning skilLS

 Prioritization  

Response Inhibition

Sustained Attention

instructional strategy

Manipulatives

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

_________

LEARNING PREFERENCES

academic skill

Grade 6 – 9

Multiplication and Division: proportions and fractions

Grade	Curriculum Focus
6-7	Solve problems involving fractions, including those requiring multiple steps or multiple operations
8	Compare proportional situations and determine unknown values in proportional situations
9	Apply an understanding of unit fractions and their relationship to other fractional amounts, in various contexts, including the use of measuring tools

Lesson Objective, Goal and Success Criteria

Lesson Objectives

1. Construct proportion puzzles by identifying given ratios and unknown values.
2. Apply proportional reasoning skills to arrive at accurate solutions to proportional puzzles.

Lesson Goal

• 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

Success Criteria

1. Accurately represent proportions using pattern blocks
2. Solve proportional puzzles through visual representations

UDL Instruction

FULL CLASS AND HANDS ON ACTIVITY – 10 minutes

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

PAIRED AND HANDS ON ACTIVITY – 10 minutes

• Working in pairs, students will solve a puzzle provided by the teacher (see supplementary worksheets). 
• 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

FULL CLASS DISCUSSION – 10 minutes

• 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

FULL DISCUSSION- 10 minutes

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

Required Materials

Laptop and presentation screen- $0 Pattern blocks- $ Fraction strips- $ Knowledgehook- $

References

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.

Additional Resources

Using the CRA Approach

The Best Hands on Fraction Activity Ever

Teaching Fractions Using Manipulatives

Knowledgehookhttps://www.knowledgehook.com/

Supplemental Documents

Introduction Activity

Partner Puzzles

Grade 6

Grade 7

Grade 8

Grade 9

Application of Differentiated Instruction- Independent Practice

Grade 6-8 

Create a person using exactly 15 pattern blocks. The total value should be more than 5 and less than 8. The value of the hexagon is 1 whole. 

Grade 9

There were 10 blocks. The total value of the blocks were 2 ⅔. What are the missing blocks? Explain how you know these were the missing pattern blocks.

Measurement of Success- Knowledgehook questions 

Grade 6

Grade 7

Grade 8-9