Enable children of all backgrounds to move beyond their current knowledge base and make culturally relevant mathematical connections.

Grades: PreK to 2nd, 6th to 8th, 3rd to 5th, Pre K to 2nd

Num & Ops Base Ten

Algebraic Thinking

Number & Operations

Counting & Cardinality

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Generate and analyze patterns.

Use place value understanding and properties of operations to add and subtract.

Understand place value.

Add and subtract within 20.

Extend the counting sequence.

Understand and apply properties of operations and the relationship between addition and subtraction.

Represent and solve problems involving addition and subtraction.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Count to tell the number of objects.

Know number names and the count sequence.

K.CC.A.1, K.CC.A.2, K.CC.A.3, K.CC.B.5, K.CC.B.4a, K.CC.B.4b, K.CC.B.4c, K.OA.A.5, 1.OA.A.2, 1.OA.B.4, 1.OA.C.6, 1.NBT.A.1, 1.NBT.C.4, 2.OA.B.2, 2.NBT.A.2, 2.NBT.B.5, 2.NBT.B.6, 2.NBT.B.7, 2.NBT.B.9, 3.NBT.A.2, 4.OA.C.5, 4.NBT.B.4

First graders in an urban public school actively engage with math by using the story
*Bean Thirteen*
as a context for developing number sense.

Grades: Pre K to 2nd, PreK to 2nd, 6th to 8th, 3rd to 5th

Algebraic Thinking

Num & Ops Base Ten

Number & Operations

Work with equal groups of objects to gain foundations for multiplication.

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Gain familiarity with factors and multiples.

Use the four operations with whole numbers to solve problems.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Multiply and divide within 100.

Represent and solve problems involving multiplication and division.

Use place value understanding and properties of operations to add and subtract.

Add and subtract within 20.

Represent and solve problems involving addition and subtraction.

Understand and apply properties of operations and the relationship between addition and subtraction.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

K.OA.A.2, K.OA.A.5, 1.OA.A.1, 1.OA.A.2, 1.OA.B.4, 1.OA.C.6, 2.OA.A.1, 2.OA.B.2, 2.NBT.B.5, 2.NBT.B.6, 2.NBT.B.7, 2.NBT.B.9, 3.OA.A.2, 3.OA.C.7, 3.OA.D.8, 3.NBT.A.2, 4.OA.A.3, 4.OA.B.4, 4.NBT.B.4, 4.NBT.B.6, 2.OA.C.3, 2.OA.C.4

How do classroom behavioral expectations support the development of students’ mathematical reasoning? A sixth-grade teacher and his students developed this example while discussing a ratio comparison problem.

Grades: 3rd to 5th, PreK to 2nd, 6th to 8th, Pre K to 2nd

Num & Ops Fractions

Ratio & Proportion

Geometry

Use equivalent fractions as a strategy to add and subtract fractions.

Understand ratio concepts and use ratio reasoning to solve problems.

Reason with shapes and their attributes.

1.G.A.3, 2.G.A.3, 3.G.A.2, 6.RP.A.1, 6.RP.A.2, 6.RP.A.3a, 6.RP.A.3b, 5.NF.A.2