A Grade-by-Grade Progression of “A Story of Units”

1. A Grade-by-Grade Progression of “A Story of Units” Scott Baldridge Common Core August 14, 2012 Part 2 of 2 (Grades 3 – 5)

2. Third Grade • Module 1: Rounding and word problemsPVComparisonRoundingBar Models • Place value units: • 534 = 5 hundreds 3 tens 4 ones = 53 tens 4 ones = 5 hundreds 34 ones • 6 tens = 6 x 10 = 60

3. Third Grade • Module 2 and Module 4 • Module 5: Multiplication and Area Module 2: ×/÷ by 2, 3, 4, 5, 10 Module 3: Measurements Module 4: ×/÷ by 6, 7, 8, 9 Module 5: Area

4. Third Grade • 0 • 0 • 1 • 1 • 2 • 2 • 3 • 3 • 1 third • 1 three A “three” unit A “third” unit

5. Third Grade • Count by: 1 third, 2 thirds, 3 thirds, … • Equivalent fractions as unit conversion: • 3 tens = 30 ones • 2 thirds = 4 sixths • Module 7: Quadrilaterals and Perimeter

6. Fourth Grade Module 1: “Big” units and the addition/subtraction algorithms Module 2: Converting metric units—An opportunity to practice mental math and the algorithms!4 × (1 m 2 cm) = 4 m 8 cm 4 × (1 ten 2 ones) = 4 tens 8 ones, leading to the 1-digit multiplication algorithm of Module 3

7. Fourth Grade Module 4: Geometry is one of the keys that unlocks Algebra

8. Fourth Grade • Module 5: Fraction operations • 3 fourths x 10 = 30 fourths(3 apples x 10 = 30 apples, 3 tens x 10 = 30 tens) • Decimals are a type of fraction, 0.1 = 1/10, but is treated like every other type of unit:30 hundredths = 3 tenths

9. Fourth Grade The last module explores multi-digit multiplications, anticipating the full algorithm in grade 5

10. Fifth Grade Module 1: Decimal number operations: Students practice and hone their 1-digit algorithms in the context of decimal numbers.

11. Fifth Grade Module 2: All other algorithms are employed in dividing by 2-digit numbers, either in the process or the checking of the answer. Division by a 2-digit number includes estimation strategies, error correction, and successive approximation

12. Fifth Grade Fraction arithmetic is modeled through the use of number lines and area models Place value also helps:8 ninths ÷ 2 = 4 ninths8 tenths ÷ 2 = 4 tenths

13. Fifth Grade Bar models start to bloom:

14. Fifth Grade • Module 5: Area and Volume • Continue to practice ×/÷ of fractions using area problems as the context • Can begin to ask the question: How does area (or volume) change when a rectangle is scaled by a whole number or fractional scale factor?

15. Fifth Grade • Coordinate plane follows a PK-6 curriculum sequence:“Number Stairs”BarGraphsLinePlotsLine Graphs • Last module knocks on the door of “slope”, leading to…

16. A Story of Ratios

17. Finish!