Minnesota

Data and Probability

• Data Sciences: Identify, formulate and investigate statistical questions by collecting data considering cultural perspectives, analyzing and interpreting data and communicating the results.

  • 2.1.1.1 Notice and describe patterns in data-rich situations and create statistical investigative questions.

    • Interpret picture graphs (2-FF.4)
    • Interpret bar graphs II (2-FF.9)
    • Interpret line plots (2-FF.12)

  • 2.1.1.2 Determine what counts as data to answer a statistical investigative question. Recognize that people collect data to answer questions and that data can vary.

  • 2.1.1.3 Collect and use data to consider and decide what data will answer a question. Represent the data as drawings, picture graphs, dot plots (a.k.a. line graphs or line plots) and with technology. Communicate observations.

    • Create picture graphs (2-FF.3)
    • Create line plots (2-FF.11)

  • 2.1.1.4 Make predictions using patterns from data visualizations.

• Chance and Uncertainty: Apply and explain the concepts of probability to interpret data, generate questions, predict and make informed decisions to solve problems and communicate ideas.

  • 2.1.2.1 Describe the difference between possible and likely.

    • More, less, and equally likely (2)

Spatial Reasoning

• Measurement: Investigate measurement using a variety of tools, units, systems, processes and techniques in various cultures. Explain and reason with attributes, estimations and formulas to communicate measurement(s) and relationships effectively. Justify decisions and consider the reasonableness of the measurement.

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

    • Estimate lengths with inches and feet (2-GG.4)
    • Which customary unit of length is appropriate: inches or feet? (2-GG.7)
    • Estimate lengths with centimeters and meters (2-HH.3)
    • Which metric unit of length is appropriate? (2-HH.5)

  • 2.2.3.2 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.

    • Measure to compare length in inches (2-GG.3)
    • Measure to compare length in centimeters (2-HH.2)

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

    • Measure using an inch ruler (2-GG.2)
    • Choose the best measuring tool: customary units of length (2-GG.9)
    • Measure using a centimeter ruler (2-HH.1)
    • Choose the best measuring tool: metric units of length (2-HH.6)

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

    • Number lines - up to 100 (2-A.2)
    • Number lines - up to 1,000 (2-A.3)
    • Addition sentences using number lines - sums to 20 (2-F.5)
    • Subtraction sentences using number lines - up to 20 (2-H.2)
    • Addition and subtraction sentences using number lines - up to 20 (2-J.1)
    • Use number lines to add two-digit numbers (2-M.4)
    • Use number lines to subtract two-digit numbers (2-O.4)

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

    • Tile a rectangle with squares (2-KK.1)
    • Count the number of squares in a rectangle (2-KK.2)
    • Area (2-KK.3)

  • 2.2.3.6 Use addition and subtraction, within 100, to solve contextual situations involving lengths that are given in the same units using drawings (such as rulers) and equations with a symbol for the unknown number to represent the situation.

    • Compare lengths: customary units (2-GG.10)
    • Customary units of length: word problems (2-GG.11)
    • Compare lengths: metric units (2-HH.7)
    • Metric units of length: word problems (2-HH.8)

  • 2.2.3.7 Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount, using $ and ¢ symbols appropriately.

    • Exchanging coins - with pictures (2)
    • Names and values of common coins (2-AA.1)
    • Count money - groups of like coins (2-AA.3)
    • Count money - pennies, nickels, and dimes only (2-AA.4)
    • Count money up to $1 (2-AA.5)
    • Equivalent amounts of money up to $1 (2-AA.6)
    • Exchanging money (2-AA.8)
    • Exchanging money II (2-AA.9)
    • Least number of coins (2-AA.10)
    • Do you have enough money? - up to $1 (2-AA.11)
    • How much more to make a dollar? (2-AA.12)

• Geometry: Analyze characteristics of geometric shapes to make mathematical arguments and justifications about geometric relationships. Use visualization and geometric modeling to compare, solve problems and communicate ideas.

  • 2.2.4.1 Classify two- and three-dimensional figures according to the number and shape of faces and the number of sides, edges and vertices.

    • Count sides and vertices (2-II.1)
    • Identify quadrilaterals (2-II.2)
    • Identify pentagons (2-II.3)
    • Name polygons: up to 6 sides (2-II.4)
    • Classify polygons: up to 6 sides (2-II.5)
    • Sort two-dimensional shapes (2-II.8)
    • Cubes (2-JJ.1)
    • Select three-dimensional shapes (2-JJ.2)
    • Name the three-dimensional shape (2-JJ.3)
    • Count vertices, edges, and faces (2-JJ.4)
    • Compare vertices, edges, and faces (2-JJ.5)
    • Identify faces of three-dimensional shapes (2-JJ.6)
    • Identify shapes traced from solids (2-JJ.7)
    • Sort three-dimensional shapes (2-JJ.8)
    • Three-dimensional shapes in the real world I (2-JJ.9)
    • Three-dimensional shapes in the real world II (2-JJ.10)
    • Three-dimensional shapes in real-world objects (2-JJ.)

  • 2.2.4.2 Create a representation for basic two-dimensional shapes such as squares, circles, triangles, rectangles, trapezoids and hexagons.

    • Draw polygons (2-II.9)

  • 2.2.4.3 Describe the location of an object in relation to another object.

    • Left, middle, and right (2)
    • Above and below (2)
    • Beside and next to (2)

Patterns and Relationships

• Number Relationships: Describe, interpret and use quantities, relationships between quantities, representations of quantities, and number systems. Describe operations and the relationship between operations. Use strategies and procedures accurately, efficiently and flexibly. Assess the reasonableness of the results.

  • 2.3.5.1 Count collections of objects using groups of 10s and 100s to 1,000. Represent the counting strategy and the total using words, symbols and pictures.

    • Skip-count by tens (2-C.3)

  • 2.3.5.2 Read, write, compare, order and represent whole numbers up to 1,000. Representations may include numerals, expanded notation, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives such as bundles of sticks, ten frames and base 10 blocks.

    • Number lines - up to 100 (2-A.2)
    • Number lines - up to 1,000 (2-A.3)
    • Compare numbers up to 1,000 using number lines (2-B.)
    • Comparing numbers up to 1,000 (2-B.3)
    • Compare and order numbers up to 1,000 using number lines (2-B.)
    • Put numbers up to 1,000 in order (2-B.4)
    • Spell word names for numbers up to 20 (2-D.1)
    • Writing numbers up to 100 in words - convert words to digits (2-D.2)
    • Writing numbers up to 100 in words - convert digits to words (2-D.3)
    • Writing numbers up to 1,000 in words - convert words to digits (2-D.4)
    • Writing numbers up to 1,000 in words - convert digits to words (2-D.5)
    • Writing numbers up to 1,000 in words (2-D.6)
    • Place value models - tens and ones (2-L.1)
    • Place value models - up to hundreds (2-L.2)
    • Convert from expanded form - up to hundreds (2-L.14)
    • Convert between standard and expanded form (2-L.15)

  • 2.3.5.3 Given a three-digit number, mentally find 10 more or 10 less and 100 more or 100 less than the number. Justify reasoning by referencing a model.

    • Add 10 or 100 to a three-digit number (2-T.1)
    • Subtract 10 or 100 from a three-digit number (2-V.1)

  • 2.3.5.4 Recognize and describe the place value of numbers between 10 and 1,000 as a relationship of groups of tens, hundreds and thousands plus an amount of a single digit. Know that 100 is 10 tens and a thousand is 10 hundreds or 100 tens.

    • Identify a digit up to the hundreds place (2-L.4)
    • Value of a digit - tens and ones (2-L.5)
    • Value of a digit - up to hundreds (2-L.6)
    • Convert to/from a number - tens and ones (2-L.8)
    • Regroup tens and ones - ways to make a number (2-L.9)
    • Regroup tens and ones (2-L.10)
    • Convert to/from a number - up to hundreds (2-L.11)
    • Convert between place values - ones and hundreds (2-L.12)
    • Convert between place values - ones, tens, and hundreds (2-L.13)
    • Regroup hundreds, tens, and ones - ways to make a number (2-L.16)

  • 2.3.5.5 Estimate sums and differences of two-digit numbers.

    • Estimate sums (2-Z.4)
    • Estimate differences (2-Z.5)

  • 2.3.5.6 Use addition and subtraction, within 1,000, to solve contextual situations using concrete models or drawings based on place value, properties of operations and/or the relationship between addition and subtraction. Relate the strategy to a written method.

    • Addition word problems - sums to 20 (2-G.4)
    • Addition sentences for word problems - sums to 20 (2-G.5)
    • Addition word problems - three one-digit numbers (2-G.10)
    • Addition word problems - four or more one-digit numbers (2-G.12)
    • Subtraction word problems - up to 20 (2-I.3)
    • Subtraction sentences for word problems - up to 20 (2-I.4)
    • Comparison word problems - up to 20 (2-K.1)
    • Use models to solve addition and subtraction word problems - up to 20 (2-K.2)
    • Addition and subtraction word problems - up to 20 (2-K.3)
    • Write number sentences for word problems - up to 20 (2-K.4)
    • Match word problems to addition and subtraction sentences - up to 20 (2-K.5)
    • Two-step addition and subtraction word problems - up to 20 (2-K.6)
    • Addition word problems - up to two digits (2-N.8)
    • Write the addition sentence - up to two digits (2-N.11)
    • Addition word problems - three numbers up to two digits each (2-N.16)
    • Addition word problems - four numbers up to two digits each (2-N.19)
    • Subtraction word problems - up to two digits (2-P.10)
    • Write the subtraction sentence - up to two digits (2-P.12)
    • Use models to solve addition and subtraction word problems - up to 100 (2-R.1)
    • Addition and subtraction word problems - up to 100 (2-R.2)
    • Match addition and subtraction word problems to equations - up to 100 (2-R.3)
    • Two-step addition and subtraction word problems - up to 100 (2-R.4)
    • Addition word problems - up to three digits (2-T.8)
    • Write the addition sentence - up to three digits (2-T.10)
    • Subtraction word problems - up to three digits (2-V.9)
    • Write the subtraction sentence - up to three digits (2-V.11)
    • Addition and subtraction word problems - up to 1,000 (2-W.5)

  • 2.3.5.7 Use a range of strategies and algorithms based on knowledge of place value and equality to flexibly add and subtract two-digit numbers. Strategies may include decomposition, expanded notation and partial sums and differences. Use place value and properties of operations to explain why strategies work.

    • Break apart a one-digit number to add (2-M.1)
    • Use models to add a two-digit and a one-digit number - without regrouping (2-M.2)
    • Use models to add a two-digit and a one-digit number - with regrouping (2-M.3)
    • Use number lines to add two-digit numbers (2-M.4)
    • Break apart a two-digit number to add - sums to 100 (2-M.5)
    • Use compensation to add on a number line - up to two digits (2-M.6)
    • Use compensation to add - up to two digits (2-M.7)
    • Use models to add two-digit numbers - without regrouping (2-M.8)
    • Use models to add two-digit numbers - with regrouping (2-M.9)
    • Use place value to add two-digit numbers - without regrouping (2-M.10)
    • Use place value to add two-digit numbers - with regrouping (2-M.11)
    • Add a two-digit and a one-digit number - without regrouping (2-N.1)
    • Add a two-digit and a one-digit number - with regrouping (2-N.2)
    • Add a multiple of 10 to a two-digit number (2-N.3)
    • Add two-digit numbers without regrouping - sums to 100 (2-N.4)
    • Add two-digit numbers with regrouping - sums to 100 (2-N.5)
    • Add two-digit numbers - sums to 100 (2-N.6)
    • Add two-digit numbers vertically - sums to 100 (2-N.7)
    • Ways to make a number using addition (2-N.9)
    • Complete the addition sentence - up to two digits (2-N.10)
    • Add two-digit numbers - sums to 200 (2-N.13)
    • Add two-digit numbers vertically - sums to 200 (2-N.14)
    • Add three numbers up to two digits each (2-N.15)
    • Add four numbers up to two digits each (2-N.17)
    • Add three or four numbers vertically - up to two digits each (2-N.18)
    • Break apart a one-digit number to subtract (2-O.1)
    • Use models to subtract a one-digit number from a two-digit number - without regrouping (2-O.2)
    • Use models to subtract a one-digit number from a two-digit number - with regrouping (2-O.3)
    • Break apart a two-digit number to subtract (2-O.5)
    • Use compensation to subtract on a number line - up to two digits (2-O.6)
    • Use compensation to subtract - up to two digits (2-O.7)
    • Use models to subtract two-digit numbers - without regrouping (2-O.9)
    • Use models to subtract two-digit numbers - with regrouping (2-O.10)
    • Use place value to subtract two-digit numbers - without regrouping (2-O.11)
    • Use place value to subtract two-digit numbers - with regrouping (2-O.12)
    • Subtract a one-digit number from a two-digit number - without regrouping (2-P.1)
    • Subtract a one-digit number from a two-digit number - with regrouping (2-P.2)
    • Subtract a one-digit number from a two-digit number (2-P.3)
    • Subtract a multiple of 10 from a two-digit number (2-P.4)
    • Subtract two-digit numbers - without regrouping (2-P.5)
    • Subtract two-digit numbers - with regrouping (2-P.6)
    • Subtract two-digit numbers (2-P.7)
    • Subtract two-digit numbers vertically (2-P.8)
    • Ways to make a number using subtraction (2-P.9)
    • Complete the subtraction sentence - up to two digits (2-P.11)
    • Add and subtract numbers - up to 100 (2-Q.1)
    • Add and subtract with two-digit numbers vertically (2-Q.2)
    • Which sign (+ or -) makes the number sentence true? - up to 100 (2-Q.3)
    • Ways to make a number using addition and subtraction - up to 100 (2-Q.4)
    • Relate addition and subtraction sentences - up to two digits (2-Q.5)
    • Complete the addition or subtraction sentence - up to 100 (2-Q.6)
    • Which addition or subtraction equation is true? - up to 100 (2-Q.8)
    • Related addition facts (2-Y.2)
    • Related subtraction facts (2-Y.3)
    • Fact families (2-Y.4)
    • Fact families - up to 100 (2)

  • 2.3.5.8 Fluently add and subtract, within 20, using mental strategies that include incrementing, compensation or fact families.

    • Add doubles (2-F.2)
    • Add doubles - complete the sentence (2-F.3)
    • Add near doubles (2-F.4)
    • Add by counting on - sums to 20 (2-F.6)
    • Make ten to add (2-F.7)
    • Add zero (2-F.8)
    • Add one-digit numbers - sums to 10 (2-G.1)
    • Add one-digit numbers - sums to 20 (2-G.2)
    • Sort addition facts - sums to 20 (2-G.3)
    • Complete the addition sentence - sums to 20 (2-G.6)
    • Which addition sentence is true? - sums to 20 (2-G.8)
    • Add three one-digit numbers (2-G.9)
    • Subtract doubles (2-H.1)
    • Subtract by counting back - up to 20 (2-H.3)
    • Use ten to subtract (2-H.4)
    • Subtract by counting on - up to 20 (2-H.5)
    • Count on and use ten to subtract - up to 20 (2-H.6)
    • Subtract zero or all (2-H.7)
    • Subtract one-digit numbers - up to 10 (2-I.1)
    • Subtract a one-digit number from a two-digit number up to 20 (2-I.2)
    • Complete the subtraction sentence - up to 20 (2-I.5)
    • Which subtraction sentence is true? - up to 20 (2-I.7)
    • Addition and subtraction - up to 20 (2-J.2)
    • Ways to make a number using addition and subtraction - up to 20 (2-J.3)
    • Which addition or subtraction sentence is true? - up to 20 (2-J.5)
    • Add in any order (2-Y.1)
    • Ways to make a number using addition - sums to 10 (2)
    • Ways to make a number using subtraction - up to 10 (2)

  • 2.3.5.9 Use landmarks of 10 to fluently add to 100 and subtract from 100.

    • Complete the addition sentence - make 100 (2)

  • 2.3.5.10 Represent and solve contextual equal sharing situations where a whole number of items is shared equally among 2 or 4 groups. Name the fractional amount using the words "halves" and "fourths." Recognize that equal shares of identical wholes need not have the same shape.

    • Identify halves and fourths (2)
    • Make halves and fourths (2)
    • Equal parts (2-LL.1)
    • Identify halves (2-LL.2)
    • Identify fourths (2-LL.4)
    • Make halves (2-LL.6)
    • Make fourths (2-LL.8)
    • Make halves in different ways (2)
    • Make fourths in different ways (2)

• Equivalence and Relational Thinking: Use concepts and properties of equivalence and relational thinking to represent and compare numerical expressions, proportional relationships, algebraic expressions and equations.

  • 2.3.6.1 Compare two- and three-digit numbers based on meanings of the hundreds, tens and ones digits.

    • Comparing numbers up to 100 (2-B.1)
    • Compare numbers up to 1,000 using number lines (2-B.)
    • Comparing numbers up to 1,000 (2-B.3)

  • 2.3.6.2 Use number sentences involving addition, subtraction and unknowns to represent given situations. Use the relationship of addition and subtraction to find values for the unknowns that make the number sentences true.

    • Complete the addition sentence - sums to 20 (2-G.6)
    • Complete the subtraction sentence - up to 20 (2-I.5)
    • Complete the addition sentence - up to two digits (2-N.10)
    • Write the addition sentence - up to two digits (2-N.11)
    • Complete the subtraction sentence - up to two digits (2-P.11)
    • Write the subtraction sentence - up to two digits (2-P.12)
    • Complete the addition or subtraction sentence - up to 100 (2-Q.6)
    • Write addition and subtraction sentences (2-Q.9)

  • 2.3.6.3 Make conjectures and justifications involving subtraction and addition with true/false and open number equations.

    • Complete the addition sentence - sums to 20 (2-G.6)
    • Balance addition equations - sums to 20 (2-G.7)
    • Which addition sentence is true? - sums to 20 (2-G.8)
    • Complete the subtraction sentence - up to 20 (2-I.5)
    • Balance subtraction equations - up to 20 (2-I.6)
    • Which subtraction sentence is true? - up to 20 (2-I.7)
    • Balance addition and subtraction equations - up to 20 (2-J.4)
    • Which addition or subtraction sentence is true? - up to 20 (2-J.5)
    • Complete the addition sentence - up to two digits (2-N.10)
    • Balance addition equations - up to two digits (2-N.12)
    • Complete the subtraction sentence - up to two digits (2-P.11)
    • Balance subtraction equations - up to two digits (2-P.13)
    • Complete the addition or subtraction sentence - up to 100 (2-Q.6)
    • Balance addition and subtraction equations - up to 100 (2-Q.7)
    • Which addition or subtraction equation is true? - up to 100 (2-Q.8)

• Patterns and Relationships: Represent and connect mathematical patterns and relationships using verbal descriptions, generalizations, tables and graphs. Use representations to generate questions, make predictions and solve mathematical problems.

  • 2.3.7.1 Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve situations in various contexts.

    • Skip-counting stories (2-C.6)
    • Skip-counting sequences (2-C.7)
    • Skip-counting puzzles (2-C.10)

  • 2.3.7.2 Recognize patterns in counting. Skip count by 2s and 5s from any given number up to 120.

    • Skip-count by twos (2-C.1)
    • Skip-count by fives (2-C.2)
    • Skip-count by tens (2-C.3)
    • Skip-count by fives and tens (2-C.4)
    • Skip-counting stories (2-C.6)
    • Skip-counting sequences (2-C.7)
    • Skip-counting puzzles (2-C.10)
    • Skip-count by twos, fives, and tens - up to 120 (2)

  • 2.3.7.3 Use numeric expressions to describe a visual growing pattern.