Grade 3

Generate questions to investigate topics of interest to students that can be answered with a variety of data or data sets.

Collect and consider data in a variety of ways including surveys, groupings, measurement, etc., and ask in what ways the data can be collected to capture as much information as necessary to inform the investigative question.

Represent data in a variety of ways including technology. Critically analyze data visualizations, including bar graphs, line plots, and scaled picture graphs with various scales. Analyze data sets with several categories by making comparisons, looking for patterns and/or making predictions and recognize the source and amount of data collected may impact the accuracy.

Interpret and communicate results, describing difference between groups, with teacher guidance. Make a statement(s) about the data collected to support the answer to the investigative question.

Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to efficiently, flexibly, and accurately solve one-step real world word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Create a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units according to the data— whole numbers, halves, or quarters.

Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

Use multiplication and division within 100 to efficiently, flexibly, and accurately solve real world word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 ×? = 48, 5 =? ÷ 3, 6 × 6 =?.

Use strategies to multiply and divide by applying and extending understanding of the properties of operations.

Demonstrate understanding of division as an unknown-factor problem.

Efficiently, flexibly, and accurately multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations.

Efficiently, flexibly, and accurately solve two-step real world word problems using the four operations. Represent these problems using visual models and equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental and estimation strategies.

Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Use place value understanding to round whole numbers to the nearest 10 or 100.

Efficiently, flexibly, and accurately add and subtract within 1000 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Understand a unit fraction as the quantity formed when a whole is partitioned into equal parts and explain that a unit fraction is one of those parts; understand fractions are quantities composed of unit fractions.

Understand a fraction as a number; and represent fractions on a number line diagram.

1. a.Represent one part of a whole divided into equal pieces on a number line by using the segment from zero to one as the whole and dividing it into equal parts based on how many pieces the whole is split into. Understand that each part has the size of one divided by the total number of parts, and that the endpoint of the first part starting at zero marks the location of this fraction on the number line.
2. b.Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

Explain equivalence of fractions and compare fractions by reasoning about their size.

1. a.Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
2. b.Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
3. c.Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
4. d.Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Recognize area as an attribute of plane figures and understand concepts of area measurement.

1. a.A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.
2. b.A plane figure which can be covered without gaps or overlaps by a certain number of unit squares is said to have an area equal to that number of square units.

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

Relate area to the operations of multiplication and addition.

1. a.Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
2. b.Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
3. c.Use tiling to show in a concrete case that the area of a rectangle with one side split into two parts is equal to the sum of the areas of two smaller rectangles. Use area models to represent the distributive property in mathematical reasoning.
4. d.Recognize area as additive. Find the area of figures made up of adjoining rectangles by decomposing them into non-overlapping rectangles and adding the areas, applying this technique to solve real world problems.

Demonstrate understanding that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

Tell and write time to the nearest minute and measure time intervals in minutes. Efficiently, flexibly, and accurately solve real world word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

Efficiently, flexibly, and accurately solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.