Grade 3 Math South Dakota Standards

Understand the denominator of a fraction represents the number of equal parts the whole is broken into.

Understand the numerator of a fraction represents the number of selected equal parts.

Understand fractions as parts of a whole, as numbers on a number line, and as multiples of unit fractions.

Use number lines and area models to explain why two fractions are equivalent and how they represent the same quantity (include fractions with denominators 2, 3, 4, 6 and 8).

Recognize and generate equivalent fractions and explain why they are equivalent.

Express whole number fractions and recognize fractions that are equivalent to whole numbers.

Compare two fractions with the same numerator or the same denominator using the symbols <, >, =.

Understand that shapes in different categories may share attributes and can define a larger category.

Understand that a quadrilateral is any four-sided shape, and identify and describe the relationships between various quadrilaterals, including trapezoids, parallelograms, rectangles, and squares.

Break apart shapes into parts with equal areas and express the area of each part as a unit fraction of the whole.

Determine whether a shape is a polygon or non-polygon.

Classify polygons based on the number of sides.

Understand area to be the amount of space inside a two-dimensional shape.

Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding unknown side lengths, and creating rectangles with the same perimeter and different areas or with the same area and different perimeters.

Measure and estimate liquid volumes using the U.S. Customary and metric system.

Measure and estimate masses of objects using the U.S. Customary and metric system.

Solve one-step addition, subtraction, multiplication, and division word problems involving masses or volumes in the same units.

Measure lengths using rulers to halves and fourths of an inch.

Tell and write time to the nearest minute using an analog and digital clock.

When solving word problems add, subtract, multiply and divide time to the minute.

Determine the value of a collection of U.S. coins and bills up to $100.00 using decimal notation.

Create a scaled table, bar graph, circle graph, and line graph to represent a given set of data.

Interpret and analyze one and two -step data problems with scaled tables, bar graphs, circle graphs, and line graphs.

Understand a square unit to be a square that is 1 unit on each side and is used to measure area.

Make a line plot using horizontal scale marked off in whole numbers, halves, or quarters.

Understand a shape has an area of 𝑛𝑛 square units if it can be covered with 𝑛𝑛 unit squares without gaps or overlaps.

Measure areas by square units.

Use tiling and visual models to explain how multiplying side lengths of a rectangle represents its area.

Solve word problems involving areas of rectangles.

Use tiling with area models to represent the distributive property of multiplication.

Understand that area can be found by adding the areas of non-overlapping rectangles and use this method to solve real-world problems.

Understand perimeter as the distance around a two-dimensional shape.

Fluently use multiplication strategies to mentally solve multiplication facts through 12.

Recall from memory multiplication facts (0-12) to include 0, 1, 2, 5, and 10.

Fluently add within 1,000 using various strategies.

Fluently subtract within 1,000 using various strategies.

Fluently multiply one-digit whole numbers by multiples of 10 in the range 10-90.

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

Compose and decompose four-digit numbers into thousands, hundreds, tens, and ones.

Read and write whole numbers up to 10,000 using standard form, word form, and expanded form.

Use visual models (e.g., arrays, equal groups, number lines) to explain and justify multiplication as combining equal groups.

Identify and explain arithmetic patterns.

Use visual models (e.g., arrays, equal groups, number lines) to explain and justify division as separating into equal groups.

Solve word problems using multiplication and division within 100 using drawings and equations with a symbol for the unknown quantities.

Determine the unknown whole number in a multiplication or division equation relating to three whole numbers.

Apply properties of operations as strategies to multiply and divide.

Understand that multiplication and division are inverse operations.

Demonstrate understanding of multiplication and division within 100 by using arrays, equal groups, and number lines to explain the relationship between the two operations.

Demonstrate understanding of addition and multiplication problems using properties (commutative, associative, and identity).

Solve two-step word problems using addition, subtraction, multiplication, and division using an equation with a symbol for the unknown quantity; Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Fractions

Geometry

Measurement

Mathematical Fluency

Numbers

Number Operations

Shapes

Data

Measurement Concepts

Time and Money

Place Value

Fraction Foundation

Operations and Algebraic Thinking

Understand 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. For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ of the area of a shape.

Tell and write time to the nearest minute and measure time intervals in minutes, using an analog and digital clock. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm³ and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step 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.

Draw 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— whole numbers, halves, or quarters.

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

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.

A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n 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.

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.

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.

Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

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.

Determine the value of a collection of money using dollar sign and decimal point appropriately. Understand that the digits to the right of the decimal represent parts of a whole dollar.

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

Fluently add and subtract within 1000 using strategies and algorithms 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 fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts (example: 1 part out of 4 equal parts is the same as ¼); understand a fraction a/b as the quantity formed by a parts of size 1/b. (example: ¾ is the same as 3 one-fourths (¼, ¼, ¼)

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

Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

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 in special cases, and compare fractions by reasoning about their size. Note - Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Recognize and generate simple equivalent fractions, e.g., ½ = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

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

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 >.

Multiply and divide within 100.

Interpret products of whole numbers, e.g., interpret 5x7 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 5x7.

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.

Use multiplication and division within 100 to solve 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.

Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.)

Understand division as an unknown-factor problem. For example, find 32÷8 by finding the number that makes 32 when multiplied by 8.

Fluently 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.

Demonstrate fluency (skill in carrying out procedures flexibly, appropriately, efficiently, and accurately) for all products of two one-digit numbers.

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order [Order of Operations]).

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Geometry

Number and Operation in Base Ten

Multiply and divide within 100.

Standards for Mathematical Practice

Solving problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Reason with shapes and their attributes.

Develop understanding of Fractions as numbers.

Represent and interpret data.

Represent and solve problems involving multiplication and division.

Operations and Algebraic Thinking

Understand properties of multiplication and the relationship between multiplication and division.

Measurement and Data

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Number and Operations — Fractions

Use place value understanding and properties of operation to perform multi-digit arithmetic.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.