Grade 2 Math Montana Standards

Reason with shapes and their attributes.

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Measure and estimate lengths in standard units.

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

Estimate lengths using units of inches, feet, centimeters, and meters.

Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Relate addition and subtraction to length.

Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram.

Work with time and money.

Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

Represent and interpret data.

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

Understand place value.

Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

100 can be thought of as a bundle of ten tens — called a "hundred."

The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

Count within 1000; skip-count by 5s, 10s, and 100s.

Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Use place value understanding and properties of operations to add and subtract.

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Add up to four two-digit numbers using strategies based on place value and properties of operations.

Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Mentally add 10 or 100 to a given number 100—900, and mentally subtract 10 or 100 from a given number 100—900.

Explain why addition and subtraction strategies work, using place value and the properties of operations.

Represent and solve problems involving addition and subtraction.

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Add and subtract within 20.

Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Work with equal groups of objects to gain foundations for multiplication.

Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

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

Recognize and draw shapes having specified attributes.

Partition a rectangle into rows and columns of same-size squares and find the total number.

Partition circles and rectangles into equal shares, recognize that equal shares need not have the same shape, and express the shares in two-halves, three-thirds, and four-fourths.

Measurement and Data

Measure the length of an object by selecting and using appropriate tools.

Organize, represent, and interpret data with up to four categories. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.

Solve addition and subtraction problems of all types using data presented.

Understand the relationship between unit sizes and number of units by measuring a single object using two different units of common measurement.

Estimate lengths using units of common measurement.

Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Use addition and subtraction within 100 to solve problems in context involving lengths that are given in the same units. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.

Represent whole numbers as lengths from 0 and represent sums and differences within 100 on a number line.

Tell and write time from analog and digital clocks to the nearest five minutes using a.m. and p.m.

Solve problems in context involving dollar bills, quarters, dimes, nickels, and pennies using $ and ¢ symbols appropriately.

Generate measurement data and present the data in multiple ways. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.

Number and Operations in Base Ten

Understand one hundred is a unit composed of ten tens and that three-digit numbers represent amounts of hundreds, tens, and ones.

Skip-count by 5s, 10s, and 100s.

Flexibly count, read, write, and represent numbers to 1000.

Compare two three-digit numbers using >, =, and < symbols.

Flexibly, accurately, and efficiently add and subtract within 100 using multiple strategies.

Add up to four two-digit numbers using multiple strategies.

Add and subtract within 1000 using multiple strategies.

Using place value, add or subtract 10 or 100 from a given number.

Understand and make connections between different strategies for addition and subtraction.

Operations and Algebraic Thinking

Use addition and subtraction within 100 to solve one- and two-step problems in context involving all problem types. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.

Flexibly, accurately, and efficiently add and subtract within 20 using mental strategies.

Determine whether a group of objects, up to 20, has an odd or even number of members.

Use addition to find the total number of objects arranged in rectangular arrays.

Standards for Mathematical Practice

Geometry

Number and Operations in Base Ten

Operations and Algebraic Thinking

Measurement and Data

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.