• # Grades Kindergarten - 5: A Story of Units

• ## Kindergarten: Kindergarten mathematics is about (1) representing, relating, and operating on whole numbers, initially with sets of objects; and (2) describing shapes and space. More learning time in Kindergarten should be devoted to number than to other topics.

• Fluency: Adding and subtracting within 5.
• Know number names and count sequence.
• Count to tell the number of objects.
• Compare numbers.
• Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
• Work with number 11-19 to gain foundations for place value. (Module 5 ~ April)

## Grade 1: First Grade mathematics is about (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.

• Fluency: Adding and subtracting within 10.
• Represent and solve problems involving addition and subtraction
• Understand and apply properties of operations and the relationship between addition and subtraction.
• Add and subtract within 20.
• Work with addition and subtraction equations.
• Extend the counting sequence.
• Understand place value.
• Using place value understanding and properties of operations to add and subtract.
• Measure lengths indirectly and by iterating length units.

## Grade 2: Second Grade mathematics is about (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.

• Fluency: Add and subtract within 20.
• Fluency: Add and subtract within 100 (with paper and pencil)
• Represent and solve problems involving addition and subtraction.
• Work with equal groups of objects to gain foundations for multiplication.
• Understand place value,
• Use place value understanding and properties of operations to add and subtract.
• Measure and estimate lengths in standard units.
• Relate addition and subtraction of length.

## Grade 3: Third Grade mathematics is about (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.

• Fluency: Multiply and divide within 100.
• Fluency: Add and subtract within 1,000.
• Represent and solve problems involving multiplication and division.
• Understand the properties of multiplication and the relationship between multiplication and division.
• Solve problems involving the four operations and identify and explain patterns in arithmetic.
• Develop understanding of fractions as numbers
• Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
• Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

## Grade 4: Fourth grade mathematics is about (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers numbers; and (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

• Fluency: Add and subtract within 1,000,000.
• Use the four operations with whole numbers to solve problems.
• Generalize place value understanding for multi-digit whole numbers.
• Use place value understanding and properties of operations to perform multi-digit arithmetic.
• Extend understanding of fraction equivalence and ordering.
• Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
• Understand decimal notations for fractions, and compare decimal fractions.

## Grade 5: Fifth grade mathematics is about (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to two-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.

• Fluency: Multi-digit multiplication
• Understand the place value system.
• Perform operations with multi-digit whole numbers and with decimals to hundredths.
• Use equivalent fractions as a strategy to add and subtract fractions.
• Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
• Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Source: A Story of Units: A Curriculum Overview and Map for grades P-5