Grade 2 Math: place value, measurement, and shapes by talking it through

A taste of a lesson on Adding and subtracting within 1000

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The 21 topics in Grade 2 Math

Each topic builds on the ones before it. The tutor checks what you already know and starts there.

1. Addition and subtraction facts within 20

   Add and subtract within 20 using mental strategies such as counting on, making ten, doubles, and using known facts to derive related ones (e.g., 8+7 = 8+2+5 = 15). Students should know from memory all sums of two one-digit numbers, and see that subtraction undoes addition (fact families). Real fluency means answering quickly and explaining the strategy used.

2. Odd and even numbers

   Determine whether a group of up to 20 objects is odd or even by pairing objects or counting by 2s; an even number has no leftover when split into two equal groups. Express an even number as a sum of two equal addends (e.g., 12 = 6 + 6). Understanding means explaining why pairing reveals a leftover of one for odd numbers.

   Builds on Addition and subtraction facts within 20

3. Shapes and their attributes

   Recognize and draw shapes by specified attributes such as number of sides, number of angles, and equal sides or faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes, and name the number of sides, angles, vertices, and faces of each. Students should see that a shape can be recognized in different sizes and orientations, and that a rhombus or square is still a quadrilateral.

4. Rectangular arrays and equal rows

   Partition a rectangle into rows and columns of same-size squares and count the total. Find totals of rectangular arrays with up to 5 rows and 5 columns by using repeated addition, and write the total as an equation with equal addends (e.g., 3 rows of 4 = 4+4+4 = 12). Understanding means seeing that rows times columns gives the same count regardless of how the array is read.

   Builds on Addition and subtraction facts within 20, Odd and even numbers

5. Halves, thirds, and fourths

   Partition circles and rectangles into two, three, or four equal shares and describe them with the words halves, thirds, fourths, half of, a third of, and a fourth of. Describe the whole as two halves, three thirds, or four fourths. Recognize that equal shares of identical wholes need not have the same shape, and that more shares means smaller shares.

   Builds on Shapes and their attributes

6. Place value to 1000

   Understand that the digits of a three-digit number stand for hundreds, tens, and ones (706 = 7 hundreds, 0 tens, 6 ones). Understand that 100 is a bundle of ten tens, and the hundreds numbers 100 through 900 are bundles of 100. Read and write numbers to 1000 in base-ten numerals, number names, and expanded form (300 + 40 + 5). Count within 1000 and skip-count by 5s, 10s, and 100s.

   Builds on Addition and subtraction facts within 20

7. Comparing three-digit numbers

   Compare two three-digit numbers by comparing hundreds digits first, then tens, then ones, and record results with >, =, and <. Students should explain why a larger hundreds digit decides the comparison even when other digits are bigger.

   Builds on Place value to 1000

8. Fluent addition and subtraction within 100

   Add and subtract within 100 fluently using place value strategies (add tens and ones separately, compensate, make a ten), properties of operations, and the relationship between addition and subtraction. Students should check answers by using the inverse operation. Includes adding up to four two-digit numbers by grouping tens and ones separately.

   Builds on Addition and subtraction facts within 20, Place value to 1000

9. Adding and subtracting within 1000

   Add and subtract within 1000 using base-ten models or drawings and place value strategies, relating each strategy to a written vertical method. Includes regrouping (trading 1 ten for 10 ones, or 1 hundred for 10 tens) and understanding why the standard algorithm works by place value. Students should be able to explain each step.

   Builds on Comparing three-digit numbers, Fluent addition and subtraction within 100

10. Mental addition and subtraction of 10 and 100

    Mentally add 10 or 100 to, and subtract 10 or 100 from, any number from 100 to 900, noticing that only the tens digit (or hundreds digit) changes and that the rest of the number stays the same, including when crossing a hundred (e.g., 380 + 10 = 390, 470 - 100 = 370).

    Builds on Place value to 1000

11. Explaining why addition and subtraction strategies work

    Explain why addition and subtraction strategies work using place value and properties of operations: commutative and associative properties, decomposing numbers, and the idea that subtraction is undone by addition. Students should justify, in their own words, why regrouping preserves the total.

    Builds on Adding and subtracting within 1000, Mental addition and subtraction of 10 and 100

12. Add and subtract word problems within 100

    Solve one- and two-step word problems involving adding to, taking from, putting together, taking apart, and comparing, with the unknown in any position (start, change, or result). Represent each with a drawing (tape diagram or bar) and an equation with a symbol for the unknown, such as 5 + ? = 12.

    Builds on Addition and subtraction facts within 20, Fluent addition and subtraction within 100

13. Number line diagrams

    Represent whole numbers as lengths from 0 on a number line with equally spaced points labeled 0, 1, 2, and so on. Show whole-number sums and differences within 100 as jumps on the number line, such as starting at 36 and jumping +10 then +5 to reach 51. Understand that the spacing between marks must be equal.

    Builds on Fluent addition and subtraction within 100

14. Measuring length with tools

    Measure the length of an object by choosing an appropriate tool (ruler, yardstick, meter stick, measuring tape) and lining up the zero point at the object's end. Measure to the nearest whole unit. Understand that the unit must be repeated end to end with no gaps or overlaps.

    Builds on Addition and subtraction facts within 20

15. Measuring with different units

    Measure the same object twice using length units of different sizes, such as paper clips and cubes or inches and centimeters, and explain why the measurement with the smaller unit is a larger number while the object is the same length. Understand that the number of units and the unit size are inversely related.

    Builds on Measuring length with tools

16. Estimating lengths with standard units

    Estimate lengths using inches, feet, centimeters, and meters by first picturing a reference object of about one unit (a paperclip is about an inch, a door about two meters) and then checking with a measurement. Understand which unit is sensible for a given object.

    Builds on Measuring length with tools

17. Measuring length differences

    Measure two objects and find how much longer one is than the other, expressing the difference in a standard length unit. Students should use a subtraction equation to represent the difference and check it by lining the objects up on a ruler.

    Builds on Fluent addition and subtraction within 100, Measuring length with tools

18. Length word problems and line plots

    Solve addition and subtraction word problems about lengths given in the same units, using ruler drawings and equations with a symbol for the unknown. Generate measurement data by measuring several objects to the nearest whole unit or by repeating a measurement, then show the data as a line plot whose horizontal scale is marked in whole units, and answer questions about the plot (how many, how many more, the most or least).

    Builds on Number line diagrams, Measuring length differences

19. Picture graphs and bar graphs

    Draw a picture graph and a bar graph with a single-unit scale for a data set with up to four categories. Use a key in picture graphs where one picture stands for more than one. Solve put-together, take-apart, and compare problems using the information in a bar graph, such as how many more one category has than another.

    Builds on Fluent addition and subtraction within 100, Add and subtract word problems within 100

20. Telling and writing time

    Tell and write time to the nearest five minutes on analog clocks (counting by fives around the dial, with the hour hand between numbers) and digital clocks, using a.m. and p.m. to tell morning from evening. Understand that the minute hand's position gives minutes past the hour, and the hour hand indicates the hour.

    Builds on Addition and subtraction facts within 20

21. Coins and dollar bills

    Know the values of pennies, nickels, dimes, quarters, and dollar bills, and count mixed collections of them. Solve word problems using $ and ¢ symbols appropriately (e.g., 65¢ or $0.65 written correctly as $0.65 with a dollar sign, and cents written with ¢). Understand that 100 cents equals one dollar.

    Builds on Fluent addition and subtraction within 100

Practice questions in Grade 2 Math

A few of the kinds of questions you will work through, with answers.