Overgeneralizing commonly accepted practices, using imprecise vocabulary, and relying on tips and tricks that do not promote conceptual mathematical understanding can lead to misunderstanding later in students’ math careers. (The fraction error in no. 6 on p. 22 has been corrected.)

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

Num & Ops Fractions

The Number System

Mathematical Practices

Num & Ops Base Ten

Algebraic Thinking

Number & Operations

Expression/Equation

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Look for and express regularity in repeated reasoning.

Look for and make use of structure.

Attend to precision.

Use appropriate tools strategically.

Model with mathematics.

Construct viable arguments and critique the reasoning of others.

Reason abstractly and quantitatively.

Make sense of problems and persevere in solving them.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Develop understanding of fractions as numbers.

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

Multiply and divide within 100.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Apply and extend previous understandings of numbers to the system of rational numbers.

Compute fluently with multi-digit numbers and find common factors and multiples.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Understand the place value system.

Write and interpret numerical expressions.

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

K.OA.A.1, 4.NBT.B.4, 4.NF.B.4a, 5.OA.A.1, 5.NBT.A.2, 5.NBT.A.3a, 5.NBT.B.7, 6.NS.B.3, 6.NS.C.5, 6.EE.A.2c, 5.NF.B.4a, 5.NF.B.4b, 2.NBT.B.5, 3.OA.C.7, 3.NBT.A.2, 3.NBT.A.3, 3.NF.A.1, 3.NF.A.3c, 4.NF.B.3a, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2, CCSS.Math.Practice.MP3, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP5, CCSS.Math.Practice.MP6, CCSS.Math.Practice.MP7, CCSS.Math.Practice.MP8, 6.NS.A.1, 5.NF.B.3, 5.NF.B.6

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