Area and the distributive property

REPRESENTATIONAL

Mathematics›Measurement|Ages 8—9|ID: mt_AQo4u7O4sM

Use tiling to demonstrate the distributive property: the area of a rectangle with sides a and (b+c) equals a×b + a×c; use area models to represent the distributive property

Mastery Evidence

Tile a 3×(4+2) rectangle and show it decomposes into 3×4 and 3×2
Use an area model to compute 6×13 as 6×10 + 6×3
Draw an area model showing 5×(7+3) = 5×7 + 5×3

Assessment Prompt

“If [child] wants to work out 6 × 13 by splitting it into 6 × 10 and 6 × 3, can they draw a rectangle divided into two parts to show why that method works?”

Prerequisites1

Understanding angles (age 8+)
hardAges 8—9

Show full prerequisite tree

Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
  Must see tiling→multiplication connection before computing area via side lengths
  - Area (age 8+) hard
    Counting unit squares is prerequisite to connecting tiling to multiplication
    - Understanding Area hard
      Must understand unit squares and area concept before measuring by counting
      - Measuring length (age 7+) soft
        Length measurement experience supports understanding area as a 2D measurement
        
        Measuring length (age 6+) hard
        Using standard measurement tools extends measuring with non-standard units
        
        Measuring length and height (age 5+) hard
        Measuring with iterated units extends Y1 beginning to measure length
        
        Comparing Lengths & Heights hard
        Measuring length with units requires first being able to compare lengths directly
        
        Measurable Attributes of Objects hard
        Comparing lengths/heights requires first identifying length as a measurable attribute
        
        Measuring length soft
        Measuring with units benefits from ability to order and compare lengths
        
        Comparing Lengths & Heights hard
        Ordering 3 objects by length and indirect comparison extends direct length comparison
        
        Measurable Attributes of Objects hard
        Comparing lengths/heights requires first identifying length as a measurable attribute
        
        Choosing measurement units soft
        Choosing appropriate tools builds on choosing appropriate units
        
        Capacity and volume hard
        Using standard units for capacity extends from beginning to measure capacity
        
        Comparing Capacity hard
        Measuring capacity with units requires first being able to compare capacities
        
        Measurable Attributes of Objects hard
        Comparing capacity requires understanding capacity as a measurable attribute
        
        Measuring length and height (age 5+) hard
        Using standard units for length extends from beginning to measure length
        
        Comparing Lengths & Heights hard
        Measuring length with units requires first being able to compare lengths directly
        
        Measurable Attributes of Objects hard
        Comparing lengths/heights requires first identifying length as a measurable attribute
        
        Measuring mass and weight hard
        Using standard units for mass extends from beginning to measure mass
        
        Measuring mass and weight (age 4+) hard
        Measuring mass with units requires first being able to compare masses directly
        
        Measurable Attributes of Objects hard
        Comparing mass/weight requires first identifying mass as a measurable attribute

Unlocks2

Fractions on a number line
softAges 8—9
Long multiplication
softAges 9—10