Grade 3 Math Michigan standards Standards

Number and Operations—Fractions

Geometry

Measurement and Data

Number and Operations in Base Ten

Operations and Algebraic Thinking

Standards for Mathematical Practice

Problem Solving

Students solve increasingly complex mathematical problems, making productive use of algebra and functions.

Using Measurement and Data

Students demonstrate increasingly complex understanding of measurement, data and analytic procedures.

Geometry

Students demonstrate increasingly complex spatial reasoning and understanding of geometric principles.

Number and Operations - Fractions

Number and Operations in Base 10

Operations and Algebraic Thinking

Students demonstrate increasingly complex understanding of number sense.

Reason with shapes and their attributes.

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.

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

Tell and write time to the nearest minute and measure time intervals in minutes. 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). 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.

Represent and interpret data.

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.

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

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.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

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.

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

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.

Develop understanding of fractions as numbers.

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

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.

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., 1/2 = 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 <, and justify the conclusions, e.g., by using a visual fraction model.

Represent and solve problems involving multiplication and division.

Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.

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.

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

Apply properties of operations as strategies to multiply and divide.

Understand division as an unknown-factor problem.

Multiply and divide within 100.

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. By the end of Grade 3, know from memory all products of two one-digit numbers.

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

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.

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.

Describe attributes of two-dimensional shapes.

Recognize that shapes can be partitioned into equal areas.

The student can describe the attributes (i.e., number of sides, corners, angles) of common two-dimensional shapes.

The student can identify shapes that can be partitioned into equal parts when provided with a visual model (limited to halves, thirds, and fourths).

The student can identify a circle, a square, and a triangle.

The student can recognize one-half of a shape.

The student can identify a side or an angle in a common two-dimensional shape.

The student can identify shapes that are divided equally when given a visual model (limited to halves and fourths).

Tell time to the hour on a digital clock.

Identify the appropriate measurement tool to solve one-step word problems involving mass and volume.

Use picture or bar graph data to answer questions about data.

Measure length of objects using standard tools, such as rulers, yardsticks, and meter sticks.

The student can tell time to the hour on a digital clock.

The student can identify tools used to measure mass (scale) and/or volume (measuring cups).

The student can use a bar graph or a simple pictograph to answer questions about data.

The student can use a ruler to measure length to the nearest whole unit.

The student can recognize that a clock is used to measure time.

The student can identify a tool used to measure a solid (i.e., scale or ruler) when presented within a context where the appropriate measurement tool is needed.

The student can identify 2 objects that share a common attribute when presented within a context.

The student can identify the object that is longer or shorter when presented with objects that have extreme differences in length.

The student can identify the hour on a digital clock.

The student can identify tools used to measure mass (scale) and volume (measuring cups).

The student can organize data using pictures or concrete objects that can be collected and sorted (maximum of 10 objects and 1 attribute).

The student can identify the length of an object measured using informal (nonstandard) units.

Use decade numbers (10, 20, 30) as benchmarks to demonstrate understanding of place value for numbers 0-30.

Demonstrate understanding of place value to tens.

Count by tens using models such as objects, base ten blocks, or money.

The student can identify correct representations of whole numbers to 50 using models, such as base 10 blocks, coins, etc.

The student can count by tens to 100 using objects, base ten blocks or money.

The student can differentiate between more and less when given two sets of objects with extreme differences.

The student can identify a single group of ten (using objects or a model) when compared with another quantity that is limited to no more than 5.

The student can identify decade numbers to 50 (10, 20, 30, 40, 50) represented with models or concrete objects.

The student can count by tens to 50 using base ten blocks or money.

Differentiate a fractional part from a whole.

The student can use a model to identify a given unit fraction (limited to one-half and onefourth).

The student can differentiate between a whole object and some of an object.

The student can use a model or concrete objects to identify a whole object or one-half of an object.

Use repeated addition to find the total number of objects and determine the sum.

Solve addition and subtraction problems when result is unknown, limited to operands and results within 20.

Solve one-step real-world problems using addition or subtraction within 20.

Identify arithmetic patterns.

The student can use repeated addition (using the same number) to find a sum up to 20.

The student can solve addition and subtraction problems with sums and differences 0 to 20.

The student can solve one-step real world problems using addition or subtraction with sums and differences within 20.

The student can create, describe and extend simple number patterns.

The student can distinguish between more and less (fewer).

The student can recognize numbers 1-5 when compared with non-numeric symbols or objects.

The student can solve one-step real world problems using counting with quantities up to 5.

The student can recognize same or different within a simple pattern involving objects or symbols.

The student can add equal groups of objects to find the sum of objects to 10.

The student can solve addition and subtraction with sums and differences within 10.

The student can solve one-step real world problems using addition or subtraction with sums/differences within 10.

The student can create, describe, and/or extend simple number patterns or patterns involving objects or symbols.