Michelle A. Doucette Onondaga Community College Syracuse, New York A Story of Units Foundations to Fraction Operations

Units Introduced in Grades K - 5 Number Geometry Kindergarten Ones Shapes composed to make composite shapes First Grade Ones and tensShapes decomposed into halves & fourths Second Grade Hundreds Thirds Unit fractions (1 whole = 3 thirds)

Third Grade 2s, 3s, 4s, 6s, 7s, 8s, 9s Unit squares Fractions in numerical form Area models including sixths and eighths Fractional units of ½ & ¼ Unit and non-unit fractions on a line plot Whole numbers as fractions Fractional units on a number line. Fourth Grade Numbers up to 1 million 1/360 of a circle as a Fractions : tenths, fifths, “one degree angle” twelfths, hundredths Decimals: tenths and hundredths, including mixed numbers Fifth Grade Numbers up to three decimal places Units on the coordinate Billions plane Number Geometry

Composing and Decomposing a whole. Examine the big idea of one arithmetic for whole numbers and fractions.

Kindergarten Complete a unit Decomposing a Whole Draw dots to make ten. Fill in the number sentence. + = = 10 Trace to make a shape. How many ways did you use? I used ___ shapes.

Kindergarten Decompose a Higher Value Unit to Subtract 10 3

First Grade Students use “make ten” or take from ten strategies. Children must know kindergarten concepts: 1. Partners of Decompositions of 1 – 9 3. Teen are composted of 10 ones and some more ones.

First Grade Composing a Higher Value Unit to Add Decomposing a Whole into Equal Parts Solve. Write the bond for the related 10 fact = ____ = __ Y/N __

Second Grade Composing a Higher Value Unit to Add Decomposing a higher value to Subtract. Add by drawing a number bond to make a hundred. Write the simplified number sentence and solve = 320 Using number bonds to subtract from – – 90 = = 16

Second Grade Decomposing a Whole into Equal Units Partition each rectangle into thirds. Shade the shapes as indicated. 3 thirds 2 thirds 1 third

Third Grade Write number bonds. Partition the fraction strip to show the unit fractions on the number line ½ ½

Third Grade Each shape is divided into equal parts. Name the fractional unit and then count and tell how many of those units are shaded. The fractional unit is 1 eighth. 6 eighths are shaded.

Fourth Grade Composing a Higher Value Unit to Add Monica’s WayStuart’s Way

Fourth Grade Decompose a higher value to subtract

Fifth Grade

How are these drawings related? Kindergarten /8 3/8 Third Grade

Fifth Grade Begin applying “one arithmetic” to decimals. Measurement standards were also examined in the reference document A Story of Units Foundations to Fraction Operations "A Story of Units Foundations to Fraction Operations." engage ny. common core, Inc, Web.