Grade 3 Math Montana Standards

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.

Geometry

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

Measurement and Data

Tell and write time on an analog and digital clock to the nearest minute and measure time intervals in minutes and solve word problems in context involving addition and subtraction of time intervals in minutes.

Measure and estimate liquid volumes and masses of objects using customary and metric units by adding, subtracting, multiplying, and dividing to solve one-step problems in context that involve masses or volumes that are given in the same units.

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. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch and show the data by making a line plot where the horizontal scale is marked off in appropriate units.

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

*Recognize area as an attribute of plane figures and understand concepts of area measurement by* understanding that 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.

*Recognize area as an attribute of plane figures and understand concepts of area measurement by* understanding that 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.

Relate area to the operations of multiplication and addition by:

*Relate area to the operations of multiplication and addition by* finding the area of a rectangle with whole-number side lengths by tiling it, and showing that the area is the same as would be found by multiplying the side lengths.

*Relate area to the operations of multiplication and addition by* multiplying side lengths to find areas of rectangles with whole-number side lengths while solving problems in context and representing whole-number products as rectangular areas.

*Relate area to the operations of multiplication and addition by* using tiling and area models to represent the distributive property in finding area of a rectangle with whole-number side lengths a and b+c is the sum of a x b and a x c.

*Relate area to the operations of multiplication and addition by* recognizing area as additive, finding areas of straight line figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts.

Solve problems in context 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.

Number and Operations in Base Ten

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

Flexibly, accurately, and efficiently 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 using strategies based on place value and properties of operations.

Number and Operations - Fractions

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts and 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 by:

*Understand a fraction as a number on the number line by* representing a unit fraction on a number line.

*Understand a fraction as a number on the number line by* representing a fraction as multiple copies of a unit fraction on a number line.

*Understand a fraction as a number on the number line by* representing fractions on a number line.

Understand the equivalence of fractions in special cases and compare fractions by reasoning about their size by:

*Understand the equivalence of fractions in special cases and compare fractions by reasoning about their size by* understanding two fractions as equivalent if they are the same size or the same point on a number line.

*Understand the equivalence of fractions in special cases and compare fractions by reasoning about their size by* recognizing and generating simple equivalent fractions and by demonstrating or justifying why the fractions are equivalent.

*Understand the equivalence of fractions in special cases and compare fractions by reasoning about their size by* writing whole numbers as fractions, recognizing fractions that are equivalent to whole numbers, and locating them on a number line.

*Understand the equivalence of fractions in special cases and compare fractions by reasoning about their size by* comparing two fractions with the same numerator or the same denominator by reasoning about their size and recognizing that comparisons are valid only when the two fractions refer to the same whole.

*Understand the equivalence of fractions in special cases and compare fractions by reasoning about their size by* recording the results of fraction comparisons with the symbols >, =, or < and justifying the conclusions.

Operations and Algebraic Thinking

Understand products of whole numbers as the total number found by multiplying a number of groups by the number of objects per group.

Understand whole-number quotients of whole numbers:

*Understand whole-number quotients of whole numbers* as the number of objects in each group with the total quantity divided equally into a number of shares.

*Understand whole-number quotients of whole numbers* as the number of shares when a total number of objects is partitioned into equal-sized groups.

Use multiplication and division within 100 to solve problems in context in situations involving equal groups, arrays, and measurement quantities.

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

Apply the commutative property of multiplication, associative property of multiplication, and distributive property of multiplication over addition on whole numbers as strategies to multiply.

Use division as an unknown factor problem.

Flexibly, accurately, and efficiently multiply and divide within 100, using strategies such as the relationship between multiplication and division.

Solve two-step problems in context using the four operations, represent these problems using equations with a letter standing for the unknown quantity and assess the reasonableness of answers using mental computation and estimation strategies. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.

Identify arithmetic patterns and explain them using properties of operations.

Operations and Algebraic Thinking

Number and Operations—Fractions

Number and Operations in Base Ten

Standards for Mathematical Practice

Measurement and Data

Geometry

Mathematical practice standard 1 is to problem-solve and persevere. Mathematically proficient students: make conjectures, plan, and follow solution strategies; evaluate their progress and accuracy; engage in sense-making and self-monitoring; and persevere in seeking solutions, and value alternative approaches.

Mathematical practice standard 2 is to abstract and generalize. Mathematically proficient students are able to decontextualize and symbolically represent both mathematical and non-mathematical situations to search for and analyze regularities, patterns, and structures.

Mathematical practice standard 3 is to justify and prove. Mathematically proficient students create, evaluate, justify, and refute mathematical claims in developmentally and mathematically appropriate ways.

Mathematical practice standard 4 is to model with mathematics. Mathematically proficient students: make sense of a scenario; identify a problem to be solved, and mathematize it; and apply a mathematical model to reach a solution and verify its viability.

Mathematical practice standard 5 is to represent. Mathematically proficient students recognize, use, create, interpret, and translate representations using appropriate methods and tools; and understand multiple ways of representing mathematical ideas and how they are related.

Mathematical practice standard 6 is to collaborate mathematically. Mathematically proficient students engage in mathematics as a social enterprise through discussion and collaborative inquiry where ideas are offered, debated, connected, and built upon toward solutions, shared understanding, and appreciation of other perspectives.

Mathematical practice standard 7 is to culturally connect. Mathematically proficient students recognize cultural connections and contributions to mathematics; and appreciate the role of mathematics in various cultural contexts, including those of tribally-specific Montana Indigenous Peoples.