A: Students use numbers in everyday and mathematical contexts to quantify or describe phenomena, develop concepts of operations with different types of numbers, use the structure and properties of numbers with operations to solve problems, and perform mathematical computations. Students develop number sense related to magnitude, estimation, and the effects of mathematical operations on different types of numbers. It is expected that students use numbers flexibly, using forms of numbers that best match a situation. Students compute efficiently and accurately. Estimation should always be used when computing with numbers or solving problems.

A.1: Students understand and use number notation to 10 million in numerals and words.

A.1.b: Round numbers to the place value appropriate for given contexts.

Rounding Whole Numbers (Number Line)

A.1.c: Compare and order numbers up to 10 million.

Modeling Whole Numbers and Decimals (Base-10 Blocks)

A.2: Students multiply and divide numbers up to four digits by numbers up to two digits, and by tens, hundreds, and thousands and interpret any remainders.

Multiplying Decimals (Area Model)
No Alien Left Behind (Division with Remainders)

A.3: Students solve problems requiring multiple operations (addition, subtraction, multiplication, and division) and use the conventions of order of operations (no exponents expected).

Order of Operations

A.4: Students understand, name, compare, illustrate, compute with, and use fractions.

A.4.a: Add and subtract fractions with unlike denominators.

Adding Fractions (Fraction Tiles)
Fraction Artist 2 (Area Models of Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)

A.4.b: Multiply a fraction by a whole number.

Factor Trees (Factoring Numbers)

A.5: Students understand and use number notation and place value in numbers with three decimal places.

A.5.a: Compare, order, read, round, and interpret decimals with up to three decimal places.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Comparing and Ordering Decimals
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Treasure Hunter (Decimals on the Number Line)

A.5.b: Add and subtract decimals with up to three decimal places.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

A.5.c: Multiply and divide decimals with up to three decimals places by a two-digit whole number.

Multiplying Decimals (Area Model)

A.5.d: Develop the concept of a fraction as division through expressing fractions with denominators of two, four, five, and 10, as decimals and decimals as fractions.

Fraction, Decimal, Percent (Area and Grid Models)

B: Students make measurements and collect, display, evaluate, analyze, and compute with data to describe or model phenomena and to make decisions based on data. Students compute statistics to summarize data sets and use concepts of probability to make predictions and describe the uncertainty inherent in data collection and measurement. It is expected that when working with measurements students: understand that most measurements are approximations and that taking repeated measurements reveals this variability; understand that a number without a unit is not a measurement, and that an appropriate unit must always be attached to a number to provide a measurement; understand that the precision and accuracy of a measurement depends on selecting the appropriate tools and units; and use estimation comparing measures to benchmarks appropriate to the type of measure and units.

B.1: Students understand and use measures of elapsed time, temperature, capacity, mass, and use measures of mass and weight.

B.1.a: Select and use appropriate tools and units (mass in grams, weight in pounds) for these measures.

Elapsed Time

B.1.b: Solve and justify problems with these measures.

Elapsed Time

B.2: Students read, construct, and interpret line graphs.

Distance-Time Graphs
Elevator Operator (Line Graphs)
Graphing Skills
Prairie Ecosystem

B.3: Students find and use median, mode, and range for a set of data.

Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

C: Students use measurement and observation to describe objects based on their sizes and shapes; model or construct two-dimensional and three-dimensional objects; solve problems involving geometric properties; compute areas and volumes based on object properties and dimensions; and perform transformations on geometric figures. When making or calculating measures students use estimation to check the reasonableness of results.

C.2: Students find the area of triangles and quadrilaterals.

C.2.a: Know how to derive and use the formula, A = (1/2) bh for the area of a triangle.

Area of Triangles

C.2.b: Find the area of parallelograms.

Area of Triangles

C.3: Students understand how to find the volume and surface area of rectangular prisms.

C.3.a: Know how to build solids with unit cubes and find their volume.

Balancing Blocks (Volume)

C.3.c: Know how to derive and use the formula (length x width x height) for the volume of a rectangular prism.

Balancing Blocks (Volume)

C.4: Students understand how to describe position and direction in two dimensions.

C.4.a: Locate points on the Cartesian plane.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

C.5: Students reflect, slide, and rotate plane figures.

C.5.a: Identify figures with rotational or line symmetry.

Quilting Bee (Symmetry)
Rock Art (Transformations)

C.5.c: Slide, rotate or reflect figures to create patterns or demonstrate congruence.

Rock Art (Transformations)

D: Students use symbols to represent or model quantities, patterns, and relationships and use symbolic manipulation to evaluate expressions and solve equations. Students solve problems using symbols, tables, graphs, and verbal rules choosing the most effective representation and converting among representations.

D.3: Students use tables, rules, diagrams, and graphs to represent and analyze the relationship between quantities.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Points, Lines, and Equations