Grade 5 Math (New York Next Generation)

Operations and Algebraic Thinking

• Write and interpret numerical expressions
• NY-5.OA.1 Apply the order of operations to evaluate numerical expressions.
• NY-5.OA.2 Write simple expressions that record calculations with numbers and interpret them without evaluating.
• Analyze patterns and relationships
• NY-5.OA.3 Generate two number patterns from rules, relate their terms, and graph the ordered pairs on a coordinate plane.

Number and Operations in Base Ten

• Understand the place value system
• NY-5.NBT.1 A digit in one place is worth ten times the place to its right and one tenth of the place to its left.
• NY-5.NBT.2 Use whole-number exponents for powers of ten and explain patterns in zeros and decimal point shifts.
• NY-5.NBT.3 Read, write and compare decimals to thousandths.
• NY-5.NBT.3a Read and write decimals to thousandths using numerals, number names and expanded form.
• NY-5.NBT.3b Compare two decimals to thousandths by place value, recording with >, = or <.
• NY-5.NBT.4 Round decimals to any place using place value understanding.
• Perform operations with multi-digit whole numbers and with decimals to hundredths
• NY-5.NBT.5 Fluently multiply multi-digit whole numbers using a standard algorithm.
• NY-5.NBT.6 Divide up to four-digit dividends by two-digit divisors, explaining with equations, arrays or area models.
• NY-5.NBT.7 Add, subtract, multiply and divide decimals to hundredths using models, drawings and strategies linked to written methods.

Number and Operations - Fractions

• Apply and extend previous understandings of multiplication and division to multiply and divide fractions
• NY-5.NF.3 Interpret a fraction as division of the numerator by the denominator and solve related word problems.
• NY-5.NF.5 Interpret multiplication as scaling (resizing).
• NY-5.NF.5a Compare the size of a product to one factor based on the other factor, without multiplying.
• NY-5.NF.5b Explain why multiplying by a fraction greater than 1 makes a product larger and less than 1 makes it smaller.
• NY-5.NF.6 Solve real-world problems multiplying fractions and mixed numbers, using models or equations.

Measurement and Data

• Convert like measurement units within a given measurement system
• NY-5.MD.1 Convert between units within one measurement system when given the conversion factor, in multi-step problems.
• Represent and interpret data
• NY-5.MD.2 Make line plots of measurements in halves, quarters and eighths and use fraction operations to solve problems.
• Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition
• NY-5.MD.3 Recognize volume as an attribute of solid figures measured with unit cubes.
• NY-5.MD.3a A unit cube (side 1 unit) has one cubic unit of volume.
• NY-5.MD.3b A solid packed with n unit cubes without gaps or overlaps has a volume of n cubic units.
• NY-5.MD.4 Measure volume by counting unit cubes (cubic cm, in, ft and improvised units).

Geometry

• Graph points on the coordinate plane to solve real-world and mathematical problems
• NY-5.G.1 Use perpendicular number lines (axes) to define a coordinate system and locate points with ordered pairs.
• NY-5.G.2 Graph points in the first quadrant to represent problems and interpret coordinates in context.
• Classify two-dimensional figures into categories based on their properties
• NY-5.G.3 Understand that attributes of a category of 2-D figures belong to all its subcategories.
• NY-5.G.4 Classify two-dimensional figures in a hierarchy based on their properties.