A foundational mathematics lesson for 7th grade intervention students bridging 1st and 2nd grade arithmetic. Features scaffolded addition, subtraction, and concrete multiplication models including open number lines, place-value decomposition, equal groups, and rectangular arrays.
Play Money ($10 bills & $1 bills): Counting tens and ones with cash feels mature and directly applicable to life skills rather than using colorful teddy bear counters.
Digital Number Lines & Interactive Sliders: Using Chromebook tools or Desmos number lines gives older students an adult, tech-enabled interface.
Graph Paper Highlighting: Allow students to highlight strips of 10 squares to visualize place-value groups cleanly.
Next Steps & Mastery Indicators
Level 1 Mastery Benchmark: Student can independently bridge through 10 on items 3-6 without counting one-by-one on fingers (80% accuracy).
Level 2 Mastery Benchmark: Student accurately breaks two-digit numbers into tens and ones and adds tens first (Items 8, 9, 10).
Next Target: Transitioning from drawn open number lines to mental jump strategies and standard vertical algorithms.
Page 2 of 2 • Stage 2 Answer Key
Part A
Array Inspection: Count Rows & Columns
8. Music Sampler Drum Pads
Rows (across):
Columns (down):
Equation: \( \text{Rows} \times \text{Cols} = \)
9. Athletic Gym Storage Cubbies
Rows (across):
Columns (down):
Equation: \( \text{Rows} \times \text{Cols} = \)
Part B
Array Architect: Shade the Grid
Shade rows and columns
10. Shade: 2 rows of 6 \( 2 \times 6 = \)
11. Shade: 3 rows of 4 \( 3 \times 4 = \)
Boss Challenge School Rooftop Solar Array
Problem 12
The green energy tech club is installing solar panels on the roof. They mount 4 rows of panels, with 5 panels in each row. What is the total number of solar panels installed?
Write repeated addition OR multiplication equation:
Total Panels
Page 2 of 2 • Rectangular Arrays & Grids
Praise Efficient Chunking: Celebrate when students transition from counting single items to skip-counting.
Page 1 of 2 • Multiplication Key
Educator Key Arrays & Grid Models
Rectangular Arrays — Answer Key
Rows, Columns & Dimensions • Bridging to Middle School Area
Area of Rectangles (\( A = b \cdot h \)): An array is the direct visual precursor to calculating area in geometry.
The Distributive Property: Splitting an array (e.g., a \( 4 \times 12 \) array split into \( 4 \times 10 \) and \( 4 \times 2 \)) is the foundational model for algebraic distribution: \( 4(x + 2) \).
Ratio Tables & Rates: Equal groups form the basis of proportional reasoning and unit rates.
Row vs. Column Memory Anchor
Architecture Cue: Remind students that architectural columns stand straight up and down (holding up a roof), while rows are like movie theater or stadium seats running left to right.
Turn-Around Rule: Emphasize that rotating an array 90 degrees doesn't add or subtract squares—it just swaps rows and columns (\( a \cdot b = b \cdot a \)).
