Use counting, place value understanding, and addition/subtraction of ones and tens to complete a partially filled-in number grid.

Represent three-digit numbers using concrete manipulatives and drawings, including cases with more than 9 of any unit.

Locate three-digit numbers on a number line and explain their placement.

Define estimation and its purpose. Round two-digit numbers to the nearest ten using a number line.

Round three-digit numbers to the nearest hundred using a number line.

Round three-digit numbers to the nearest ten using a number line.

Round multi-digit numbers to any place in more complex cases, including those involving real-world contexts and/or assessing the reasonableness of that estimate.

Add numbers with up to one composition within 1,000.

Add numbers with multiple compositions within 1,000.

Solve one-step word problems involving addition, using rounding to assess the reasonableness of answers.

Subtract numbers with up to one decomposition within 1,000.

Subtract numbers with multiple decompositions within 1,000.

Solve one-step word problems involving subtraction, using rounding to assess the reasonableness of answers.

Solve one- and two-step word problems involving addition and subtraction, using rounding to assess the reasonableness of answers.

Identify and create situations involving equal groups and describe these situations using the language and notation of multiplication.

Identify and create situations involving arrays and describe these situations using the language and notation of multiplication.

Identify and create situations involving unknown group size and find group size in situations.

Identify and create situations involving an unknown number of groups and find the number of groups in situations.

Relate multiplication and division and understand that division can represent situations of unknown group size or an unknown number of groups.

Build fluency with multiplication facts using units of 2, 5, and 10.

Demonstrate the commutativity of multiplication.

Build fluency with division facts using units of 2, 5, and 10.

Solve one-step word problems involving multiplication and division using units of 2, 5, and 10.

Build fluency with multiplication and division facts using units of 3.

Build fluency with multiplication and division facts using units of 4.

Solve one-step word problems involving multiplication and division using units of 3 and 4.

Determine the unknown whole number in a multiplication or division equation relating three whole numbers, including equations with a letter standing for the unknown quantity.

Solve one-step word problems involving multiplication and division and write problem contexts to match expressions and equations.

Solve two-step word problems involving multiplication and division.

Solve two-step word problems involving all four operations.

Create scaled picture graphs where the scale is provided.

Create scaled picture graphs where the scale must be determined.

Create scaled bar graphs where the scale is provided.

Create scaled bar graphs where the scale must be determined.

Solve one- and two-step word problems using information presented in scaled picture and bar graphs.

Study commutativity to find known facts of 6, 7, 8, and 9.

Understand the zero and identity properties of multiplication.

Understand the role of parentheses and apply to solving problems.

Introduce the distributive property of multiplication.

Introduce the associative property of multiplication.

Build fluency with multiplication and division facts using units of 6.

Build fluency with multiplication and division facts using units of 7.

Use the associative property as a strategy to multiply by units of 6.

Use the distributive property as a strategy to multiply by units of 6.

Use the distributive property as a strategy to multiply by units of 7.

Solve one- and two-step word problems involving units up to 7.

Build fluency with multiplication and division facts using units of 8 and 9.

Use the associative property as a strategy to multiply by units of 8 and 9.

Use the distributive property as a strategy to multiply by units of 8 and 9.

Use the distributive property as a strategy to multiply by units of 8 and 9, including the subtractive use of the distributive property.

Solve one- and two-step word problems involving units up to 9.

Multiply one-digit whole numbers by multiples of 10.

Multiply one-digit whole numbers by two-digit whole numbers using the associative and distributive properties.

Solve two-step word problems involving all four operations.

Solve two-step word problems involving all four operations, including multiplying one-digit whole numbers by multiples of 10.

Identify patterns in single or multiple rows/columns of the multiplication table.

Identify other patterns in the multiplication table.

Identify arithmetic patterns and explain them using properties of operations.

Understand that area is an attribute of plane figures that is a measure of how much flat space an object takes up. Find the area of a figure using pattern blocks, which can be used as concrete non-standard units.

Understand that area is measured using square units. Find the area of a figure using square tiles.

Find the area of a rectangle by counting unit squares on grids.

Find the area of a rectangle with incomplete information about its rows and columns of square units.

Find the area of a rectangle that has been superimposed over a grid.

Find the area of a rectangle through multiplication of the side lengths.

Understand standard units for measuring area, including square inches, square centimeters, square feet, and square meters, and choose an appropriate unit to measure the area of various rectangles.

Measure the side lengths of a rectangle to find its area.

Solve word problems involving area.

Compose and decompose a rectangle, seeing and making use of the idea that the sum of the areas of the decomposed rectangle is equal to the area of the composed rectangle.

Apply the distributive property as a strategy to find the total area of a large rectangle.

Recognize area as additive. Find the area of a composite figure as shown on a grid or with all side lengths labeled.

Recognize area as additive. Find the area of a composite figure when not all dimensions are given.

Recognize area as additive. Find the area of a complex composite figure.

Compare and classify polygons.

Compare and classify quadrilaterals.

Draw shapes with specified attributes.

Reason about composing and decomposing polygons using tangrams.

Understand perimeter to be the boundary around a two-dimensional shape. Compare perimeters of various polygons using concrete non-standard units.

Find perimeter of polygons whose sides are marked with unit length marks by counting the unit lengths.

Find perimeter of shapes with all side lengths labeled.

Find perimeter by measuring side lengths in whole number units.

Find perimeter of regular polygons and of rectangles when some side lengths are not given.

Solve word problems involving finding perimeter given the side lengths.

Find side lengths of regular polygons and of rectangles when given perimeter and other side lengths.

Solve more complex word problems involving perimeter, such as finding a missing side length given perimeter and other side lengths.

Find rectangles with the same area and different perimeters.

Find rectangles with the same perimeter and different areas.

Solve a variety of word problems involving area and perimeter.

Reason about composing and decomposing polygons with various areas and perimeters using tetrominoes.

Partition a whole into equal parts using area models, identifying fractional units.

Partition a whole into equal parts using tape diagrams (i.e., fraction strips), identifying and writing unit fractions in fraction notation.

Partition a whole into equal parts using area models and tape diagrams, identifying and writing non-unit fractions in fraction notation.

Identify fractions of a whole that is not partitioned into equal parts.

Draw the whole when given the unit fraction.

Identify a shaded fractional part in different ways, depending on the designation of the whole.

Partition a number line from 0 to 1 into fractional units.

Place any fraction on a number line with endpoints 0 and 1.

Place any fraction on a number line with endpoints 0 and another whole number greater than 1.

Place any fraction on a number line with endpoints greater than 0.

Place various fractions on a number line where the given interval is not a whole.

Understand two fractions as equivalent if they are the same point on a number line referring to the same whole. Use this understanding to generate simple equivalent fractions.

Understand two fractions as equivalent if they are the same sized pieces of the same sized wholes, though not necessarily the same shape. Use this understanding to generate simple equivalent fractions.

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Explain equivalence by manipulating units and reasoning about their size.

Compare unit fractions (a unique case of fractions with the same numerators) by reasoning about the size of their units. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <.

Compare fractions with the same numerators by reasoning about the size of their units. Record the results of comparisons with the symbols >, =, or <.

Compare fractions with the same denominators by reasoning about their number of units. Record the results of comparisons with the symbols >, =, or <.

Compare and order fractions using various methods.

Measure lengths to the nearest half inch.

Measure lengths to the nearest quarter inch.

Generate measurement data and represent it in a line plot.

Create line plots (dot plots).

Tell time to the nearest minute.

Tell time to the minute before the hour.

Relate clocks to number lines.

Solve word problems involving elapsed time within the same hour.

Solve word problems involving elapsed time that involves crossing the hour mark.

Solve word problems involving all cases of elapsed time in minutes.

Understand mass as an attribute of objects that is measured in grams and kilograms. Develop benchmarks for 1 kilogram and 1 gram.

Estimate and measure mass in grams and kilograms by reading a measurement scale on an analog scale or other scale.

Solve word problems involving masses given in the same unit.

Understand liquid volume as an attribute of objects that is measured in liters and milliliters. Develop benchmarks for 1 liter and 1 milliliter.

Estimate and measure liquid volume in liters and milliliters by reading the measurement scale on a beaker or other container.

Solve word problems involving volumes given in the same unit.