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

Scott BaldridgeScott Baldridge

Common CoreCommon Core

August 14, 2012August 14, 2012Part 2 of 2 (Grades 3 – 5)Part 2 of 2 (Grades 3 – 5)

Third GradeThird GradeModule 1: Rounding and word problemsModule 1: Rounding and word problems

PVPVComparisonComparisonRoundingRoundingBar ModelsBar Models

Place value units:Place value units: 534 = 5 hundreds 3 tens 4 ones534 = 5 hundreds 3 tens 4 ones

= 53 tens 4 ones= 53 tens 4 ones

= 5 hundreds 34 ones= 5 hundreds 34 ones

6 tens = 6 x 10 = 606 tens = 6 x 10 = 60

Third GradeThird Grade

Module 2: ×/÷ by 2, 3, 4, 5, 10Module 2: ×/÷ by 2, 3, 4, 5, 10

Module 3: MeasurementsModule 3: Measurements

Module 4: ×/÷ by 6, 7, 8, 9Module 4: ×/÷ by 6, 7, 8, 9

Module 5: AreaModule 5: Area

Module 2 and Module 4

Module 5: Multiplication and Area

Third GradeThird Grade

A “three” unitA “three” unit

A “third” unitA “third” unit0 1 2 3

1 third

0 1 2 3

1 three

Third GradeThird Grade

Count by: 1 third, 2 thirds, 3 thirds, …Count by: 1 third, 2 thirds, 3 thirds, …

Equivalent fractions as unit conversion:Equivalent fractions as unit conversion:

3 tens = 30 ones3 tens = 30 ones 2 thirds = 4 sixths2 thirds = 4 sixths

Module 7: Quadrilaterals and PerimeterModule 7: Quadrilaterals and Perimeter

Fourth GradeFourth Grade

Module 1: “Big” units and the addition/subtraction Module 1: “Big” units and the addition/subtraction algorithmsalgorithms

Module 2: Converting metric units—An opportunity Module 2: Converting metric units—An opportunity to practice mental math and the algorithms!to practice mental math and the algorithms!

4 × (1 m 2 cm) = 4 m 8 cm 4 × (1 m 2 cm) = 4 m 8 cm 4 × (1 ten 2 ones) = 4 tens 8 ones, 4 × (1 ten 2 ones) = 4 tens 8 ones,

leading to the 1-digit multiplication algorithm of leading to the 1-digit multiplication algorithm of Module 3 Module 3

Fourth GradeFourth Grade

Module 4: Geometry is one of the keys Module 4: Geometry is one of the keys that unlocks Algebrathat unlocks Algebra

Fourth GradeFourth Grade

Module 5: Fraction operationsModule 5: Fraction operations 3 fourths x 10 = 30 fourths3 fourths x 10 = 30 fourths

(3 apples x 10 = 30 apples,(3 apples x 10 = 30 apples, 3 tens x 10 = 30 tens) 3 tens x 10 = 30 tens)

Decimals are a type of fraction, 0.1 = 1/10, but is Decimals are a type of fraction, 0.1 = 1/10, but is treated like every other type of unit:treated like every other type of unit:

30 hundredths = 3 tenths30 hundredths = 3 tenths

Fourth GradeFourth Grade

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

Fifth GradeFifth Grade

Module 1: Decimal Module 1: Decimal number operations: number operations:

Students practice and Students practice and hone their 1-digit hone their 1-digit algorithms in the algorithms in the context of decimal context of decimal numbers.numbers.

Fifth GradeFifth Grade

Module 2: All other algorithms are Module 2: All other algorithms are employed in dividing by 2-digit numbers, employed in dividing by 2-digit numbers, either in the process or the checking of the either in the process or the checking of the answer.answer.

Division by a 2-digit number includes Division by a 2-digit number includes estimation strategies, error correction, and estimation strategies, error correction, and successive approximationsuccessive approximation

Fifth GradeFifth Grade

Fraction arithmetic is modeled through the Fraction arithmetic is modeled through the use of number lines and area modelsuse of number lines and area models

Place value also helps:Place value also helps:8 ninths ÷ 2 = 4 ninths8 ninths ÷ 2 = 4 ninths8 tenths ÷ 2 = 4 tenths 8 tenths ÷ 2 = 4 tenths

Fifth GradeFifth Grade

Bar models start to bloom:Bar models start to bloom:

Fifth GradeFifth Grade

Module 5: Area and VolumeModule 5: Area and Volume

Continue to practice ×/÷ of fractions using Continue to practice ×/÷ of fractions using area problems as the contextarea problems as the context

Can begin to ask the question: How does Can begin to ask the question: How does area (or volume) change when a rectangle is area (or volume) change when a rectangle is scaled by a whole number or fractional scale scaled by a whole number or fractional scale factor? factor?

Fifth GradeFifth Grade

Coordinate plane follows a PK-6 Coordinate plane follows a PK-6 curriculum sequence:curriculum sequence:

“Number Stairs”“Number Stairs”Bar GraphsBar GraphsLine Line PlotsPlotsLine GraphsLine Graphs

Last module knocks on the door of “slope”, Last module knocks on the door of “slope”, leading to… leading to…

A Story of RatiosA Story of Ratios

Finish!Finish!