Math Scope and Sequence

Key Topics in Second Grade Math:

Operations and Algebraic Thinking

Numbers and Operations (Base 10)

  • 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.
  • Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.
  • 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.
  • Find patterns in numbers such as in a 100s chart.

  • 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.
  • 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.
  • Recall and apply basic addition and subtraction facts (to 18).
  • Model addition and subtraction of two digit numbers with objects, pictures, words, and numbers.
  • Show equivalent representations for whole numbers by using addition and subtraction facts.
  • 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.
  • 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.

Measurement and Data

Geometry

  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Determine the value of a collection of coins up to one dollar.
  • 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.

Math Fact Fluency:

Counting Backwards from 100, Skip Counting by 2’s,5’s,10’s and Addition Facts

Math Units

2nd Grade

Topic

Category

Standard

Quarter

UNIT 1: Operations and Algebraic Thinking

Review of First Grade Skills

1st

Understand Math Strategies (fact families)

Operations and Algebraic Thinking

Fluently add/subtract within 20

1st

Solve One-Step Word Problems

Operations and Algebraic Thinking

Use addition/subtraction within 100 to solve word problems

1st

Understand Mental Math Strategies (Make a ten)

Operations and Algebraic Thinking

Fluently add/subtract within 20

1st

Understand Even and Odd Numbers

Operations and Algebraic Thinking; Number and Operations in Base Ten

Count within 1000; skip-counting; determine if group of objects has even/odd members

1st

Add Using Arrays

Operations and Algebraic Thinking; Number and Operations in Base Ten

Count within 1000; skip-counting; use addition to find the total number of objects in rectangular arrays

1st

Solve Two-Step Word Problems

Operations and Algebraic Thinking

Use addition/subtraction within 100 to solve word problems

1st

UNIT 1 Interim Assessment

UNIT 2: Numbers and Operations in Base Ten

Add Two-Digit Numbers

Numbers in Operations in Base Ten

Count within 1000; fluently add/subtract with 100; mentally add 10 or 100 to a give number

1st

Subtract two-digit numbers

Numbers in Operations in Base Ten

Count within 1000; fluently add/subtract with 100; mentally add 10 or 100 to a give number

1st

Solve one-step word problems with two-digit numbers

Numbers in Operations in Base Ten; Operations and Algebraic Thinking

Use addition/subtraction within 100 to solve word problems; fluently add/subtract within 100 using strategies

2nd

Understand three-digit numbers

Numbers in Operations in Base Ten

Count within 1000; skip-count by 5’s, 10’s. and 100’s; “hundred” bundle; the numbers refer to hundreds (and 0 tens/ones)

2nd

Read and write three-digit numbers

Numbers in Operations in Base Ten

Read and write numbers to 100 using base-ten numerals, numbers names, expanded form

2nd

Compare Three-digit numbers

Numbers in Operations in Base Ten

Compare 2 three-digit numbers using symbols

2nd

Add Three-Digit Numbers

Numbers in Operations in Base Ten

Add/subtract within 1000 using strategies; explain why addition/subtraction strategies work

2nd

Subtract three-digit numbers

Numbers in Operations in Base Ten

Add/subtract within 1000 using strategies; explain why addition/subtraction strategies work

2nd

Add several two-digit numbers

Numbers in Operations in Base Ten

Add numbers based on place value and properties of operations

2nd

UNIT 2 Interim Assessment

UNIT 3: Measurement and Data

Understand Length and Measurement Tools

Measurement and Data

Measure the length of objects using tools

2nd

Measure Length

Measurement and Data

Measure the length of objects using tools

2nd

Understand Measurement with different units

Measurement and Data

Measure the length twice using different units

3rd

Understand estimating length

Measurement and Data

Estimate length using units

3rd

Compare lengths

Measurement and Data

Measure then compare lengths of objects

3rd

Add and subtract lengths

Measurement and Data; Operations and Algebraic Thinking

Use addition/subtraction to solve word problems involving lengths; represent numbers on a number line

3rd

Understand reading and making line plots

Measurement and Data

Represent measurement of whole numbers on a number line and by making a line plot

3rd

Draw and use bar graphs and picture graphs

Measurement and Data

Draw a graph to show data; solve/compare information

3rd

Tell and write time

Measurement and Data; Number and Operations in Base Ten

Skip-count by 5s; tell/write time using analog/digital clocks to the nearest 5 minutes

3rd

Solve problems involving money

Measurement and Data; Number and Operations in Base Ten

Skip-count by 5s, 10s, 100s; solve word problems using money and symbols

3rd

UNIT 3 Interim Assessment

Recognize and Draw Shapes

Geometry

recognize/draw shapes with specified attributes

3rd

Understand Tiling in Rectangles

Geometry

Partition a rectangle into rows/columns

4th

Understand Halves, Thirds, and Fourths in Shapes

Geometry

Partition circles/ rectangles into equal shares

4th

UNIT 4 Interim Assessment

Diagnostic

Introduction to Multiplication/ division

Operations and Algebraic Thinking

Identify patterns on multiplication table; Interpret products/ quotients of whole numbers

4th