Arithmetic

Unit 1

• Use equivalent fractions as a strategy to add and subtract fractions with unlike denominators (²⁄₅ + ⁷⁄₃ = ⁶⁄₁₅ + ³⁵⁄₁₅ = ⁴¹⁄₁₅)
• Solve word problems with addition and subtraction of fractions or mixed numbers with like and unlike denominators
• Create models or equations to represent problems with fractions
• Understand a fraction as division of the numerator by the denominator
• Solve word problems dividing whole numbers leading to fraction or mixed number answers
• Multiply a fraction by a whole number or a whole number by a fraction
• Find areas of rectangles with fractional sides by modeling with unit squares
• Interpret multiplication as scaling (resizing)
• Explain results of multiplying a number by a fraction greater or less than 1
• Use all operations to solve world problems with fractions and mixed numbers

Unit 2

• Compute and explain division of a fraction by a whole number
• Compute and explain division of a whole number by unit fraction
• Divide unit fractions by non-zero whole numbers and whole numbers by unit fractions
• Write and interpret numerical expressions
• Evaluate simple expressions
• Analyze patterns and relationships
• Expand a whole number (2-50) as a product of its prime factors
• Analyze patterns and relationships given two rules
• Understand the coordinate system and the meanings of the origin, x-axis, x-coordinate, y-axis, and y-coordinate
• Graph points in the first quadrant of the coordinate plane to solve real-world and mathematical problems

Unit 3

• Classify two-dimensional figures into categories based on their properties
• Classify two-dimensional figures into a hierarchy
• Understand that each place in a number represents 10 times the place to right and one-tenth of the place to the left
• Know patterns of zeros when multiplying or dividing a number by powers of 10
• Use exponents to show powers of 10
• Read, write, and compare decimals to the thousandths place
• Perform operations with multi-digit whole numbers
• Perform operations with decimals to hundredths
• Convert like measurement units within a given measurement system
• Use measurement conversions in solving real world problems

Unit 4

• Use a line plot to display a data set of unit fraction measurements
• Use operations of fractions to solve problems from displayed data
• Understand concepts of volume and measuring of volume
• Relate volume to multiplication and to addition
• Define and describe a cubic unit
• Use standard or improvised unit cubes to measure volume
• Find volume of rectangular prisms by packing the prism with unit cubes
• Know and apply formulas for the volume of right rectangular prisms
• Solve real world problems involving volume
• Find volumes of solid figures that are composed of two non-overlapping right rectangular prisms