Draw aligned number lines for 6 liters of paint covering 4 square meters. Mark 0, one batch, and 6 batches. How much area do 36 liters cover?
24 square meters; aligned pairs (0,0), (6,4), (36,24)
36 ÷ 6 = 6 batches; 6 × 4 = 24.
Day 037Double Number Lines
Standards 6.RP.A.3a
LEARNING TARGET
I can represent a ratio on a double number line.
01 · LEARN
Build the idea
Place zero on both parallel number lines. Align a known pair above and below one tick. Add equal jumps on each line so aligned values remain in the same ratio.
Draw aligned number lines for 5 liters of paint covering 5 square meters. Mark 0, one batch, and 5 batches. How much area do 25 liters cover?
25 square meters; aligned pairs (0,0), (5,5), (25,25)
25 ÷ 5 = 5 batches; 5 × 5 = 25.
02 · PRACTICE
Your turn
Work in order. Start with the foundations, then build toward explanation and application.
Draw aligned number lines for 7 liters of paint covering 7 square meters. Mark 0, one batch, and 3 batches. How much area do 21 liters cover?
Draw aligned number lines for 3 liters of paint covering 3 square meters. Mark 0, one batch, and 3 batches. How much area do 9 liters cover?
Draw aligned number lines for 2 liters of paint covering 7 square meters. Mark 0, one batch, and 4 batches. How much area do 8 liters cover?
Draw aligned number lines for 7 liters of paint covering 2 square meters. Mark 0, one batch, and 3 batches. How much area do 21 liters cover?
Draw aligned number lines for 3 liters of paint covering 6 square meters. Mark 0, one batch, and 6 batches. How much area do 18 liters cover?
Draw aligned number lines for 6 liters of paint covering 4 square meters. Mark 0, one batch, and 5 batches. How much area do 30 liters cover?
Draw aligned number lines for 7 liters of paint covering 7 square meters. Mark 0, one batch, and 4 batches. How much area do 28 liters cover?
Draw aligned number lines for 5 liters of paint covering 7 square meters. Mark 0, one batch, and 6 batches. How much area do 30 liters cover?
Draw aligned number lines for 3 liters of paint covering 3 square meters. Mark 0, one batch, and 4 batches. How much area do 12 liters cover?
Draw aligned number lines for 4 liters of paint covering 7 square meters. Mark 0, one batch, and 7 batches. How much area do 28 liters cover?
03 · CHECK
Answers and reasoning
Reveal the teacher answer key
- 21 square meters; aligned pairs (0,0), (7,7), (21,21)
21 ÷ 7 = 3 batches; 3 × 7 = 21.
- 9 square meters; aligned pairs (0,0), (3,3), (9,9)
9 ÷ 3 = 3 batches; 3 × 3 = 9.
- 28 square meters; aligned pairs (0,0), (2,7), (8,28)
8 ÷ 2 = 4 batches; 4 × 7 = 28.
- 6 square meters; aligned pairs (0,0), (7,2), (21,6)
21 ÷ 7 = 3 batches; 3 × 2 = 6.
- 36 square meters; aligned pairs (0,0), (3,6), (18,36)
18 ÷ 3 = 6 batches; 6 × 6 = 36.
- 20 square meters; aligned pairs (0,0), (6,4), (30,20)
30 ÷ 6 = 5 batches; 5 × 4 = 20.
- 28 square meters; aligned pairs (0,0), (7,7), (28,28)
28 ÷ 7 = 4 batches; 4 × 7 = 28.
- 42 square meters; aligned pairs (0,0), (5,7), (30,42)
30 ÷ 5 = 6 batches; 6 × 7 = 42.
- 12 square meters; aligned pairs (0,0), (3,3), (12,12)
12 ÷ 3 = 4 batches; 4 × 3 = 12.
- 49 square meters; aligned pairs (0,0), (4,7), (28,49)
28 ÷ 4 = 7 batches; 7 × 7 = 49.