Math Handbook
for
2nd Grade
This handbook was designed to give an overview of the 2nd grade math curriculum. Based on the NYS Common Core Standards, we have provided an overview of the concepts to be covered this year. Concrete hands on provides the foundation for the concepts. Making math a part of everyday life helps students understand its application in the real world. Practice of facts and skills promotes fluency in mental math and provides a basis for concepts that will be introduced down the line.
You can help your child recognize the math of daily life by talking about it while playing math  cards and board games, applying math  in measuring  time, ingredients, size, etc., money, practicing facts in the car. In addition, there are many online math sites and apps available for free practice. Thank you for working with the second grade team to help your child be successful this year.
Contents
Number Concepts
Numbers to 1,000
Basic Facts and Relationships
Addition and Subtraction
Money and Time
Customary Measurement
Metric Measurement
Data
Geometry and Fraction Concepts
Grade 2 Overview
Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction.

Add and subtract within 20.

Work with equal groups of objects to gain foundations for multiplication.
Number and Operations in Base Ten

Understand place value.

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

Measure and estimate lengths in standard units.

Relate addition and subtraction to length.

Work with time and money.

Represent and interpret data.
Geometry

Reason with shapes and their attributes.
Mathematical Practices

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.
Number Concepts
Vocabulary
digits  the symbols used in a number system; the ten digits used in our baseten system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Numbers have 1 or more digits. 86 has 2 digits.
even numbers  whole numbers that show pairs with no cubes left over.
odd numbers  whole numbers that show pairs with cubes left over.
Even and Odd Numbers
Two make a pair.
A pair is a set of two.
6 is an even number because there are no cubes left over.
7 is an odd number because there is a cube left over.
You can predict whether a sum will be even or odd if you know whether an addend is even or odd.
odd + odd = even
even + even = even
odd + even = odd
even + odd = odd
Represent Even Numbers
An even number can be shown as two equal groups.
6= 3 + 3
8 = 4 + 4
Understand Place Value
0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are digits.
In a twodigit number you know the value of a digit by its place.
64
The digit 6 is in the tens place. It tells you there are 6 tens, or 60.
The digit 4 is in the ones place. It tells you there are 4 ones, or 4.
Tens 
Ones 
6 
4 
6 tens 4 ones
Expanded Form
Expanded form is the sum of the value of the tens digit and the ones digit.
37= 30 + 7
Numbers can be written in different ways:

Standard form  34

Word form  thirtyfour

Expanded form  30 + 4 = 34

34 = 3 tens + 4 ones
Composing and Decomposing Numbers
You can show the value of numbers in different ways.
34 can be shown as:
3 tens 4 ones
You can trade 1 ten for 10 ones
2 tens 14 ones
You can trade another ten
1 ten 24 ones
Trade the final ten
34 ones

Finding a pattern can help you find all the ways to show a all the ways to show a number with tens and ones.

Note how the patterns of tens and ones change as you trade tens for ones.

When two numbers have the same value, they are equal.
Counting patterns within 100
Each number on the chart is one more than the number that comes before and one less than the number that comes after it.
Each number is ten more than the number above it and ten less than the number below it.
Use the Hundred Chart to practice counting backwards and forwards by ones, twos, fives, and tens; identifying odd and even, and observing patterns in numbers.
Counting Patterns within a Thousand
0 1 2 3 4 5 6 7 8 9
10 20 30 40 50 60 70 80 90 100
110 120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300
thousand  a quantity equivalent to ten hundreds.
10 hundreds make 1,000
When counting by tens, the tens digit changes.
40, 50, 60  140, 150, 160
When counting by hundreds, the hundreds digit changes.
150, 250, 350, 450, 550
When counting by fives, there are only fives and zeros in the ones place.
175, 180, 185, 190, 195, 200, 205, 210
Numbers to 1,000
Vocabulary
compare – to describe whether numbers are equal to (=), greater than (>), or less than (<) one another.
is greater than (>) a symbol used to compare two numbers when the first number has the greater value.
4 > 3 47 > 38
is less than (<) a symbol used to to compare two numbers when the first number has the lesser value
3 < 4 38 < 47
is equal to (=) a symbol used to compare two numbers that have the same value
3 = 3 23 = 23 443 = 443
Comparing 3digit numbers
In comparing 3digit numbers, look at the hundreds place first
761 > 458 > 276
When the hundreds are the same, look at the tens place or the ones place for the next greater number
241 > 222 > 214
Group Tens as Hundreds
10 ones = 1 ten = 10
You can group 100 ones in groups of tens. 10 tens = 1 hundred = 100
20 tens = 2 hundreds = 200
30 tens = 3 hundreds = 300
40 tens = 4 hundreds = 400
50 tens = 5 hundreds = 500
60 tens = 6 hundreds = 600
70 tens = 7 hundreds = 700
80 tens = 8 hundreds = 800
90 tens = 9 hundreds = 900
100 tens = 10 hundreds = 1,000
You can count out 10 tens and group them together, then count out how many groups of 10 tens to know how many hundreds there are.
Explore 3Digit Numbers
You can write a 3 digit number for a group of tens.
Each group of 10 tens is counted and the number is written as the hundreds digit. The rest of the tens are written as the tens digit. A zero is written as the ones digit.
Ways to Model 3 Digit Numbers

Use base ten blocks to show hundreds, tens. and ones.

Write the digits in the chart

Show the number using blocks.

Draw a quick picture.
Hundreds 
Tens 
Ones 
4 
5 
0 
You can use a place value chart to draw a quick picture.
4 hundreds + 5 tens + 0 ones = 450
400 + 50 + 0 = 450
To write a three digit number, first write the number of hundreds blocks, then the number of tens blocks, then the numbers of ones blocks.
To know the values of digits, look at the places of the digits.
To identify the value of the 4 in each example, look at its place value.
450  The value of 4 = 400
Hundreds 
Tens 
Ones 
4 
5 
0 
540  The value of 4 = 40
Hundreds 
Tens 
Ones 
5 
4 
0 
504  The value 4 = 4
Hundreds 
Tens 
Ones 
5 
0 
4 
Use words to write 3 digit numbers.
First look at the hundreds digit .
Then look at the tens digit and the ones digit together
612
six hundred twelve
453
four hundred fifty three
You can write a 3 digit number using digits,number names, and expanded form.
Number Names
There are 10 hundreds in 1 thousand.
You can read and write numbers to 1,000 using base ten blocks, numerals, number names, and expanded form.
You can show the value of a number in different ways:
Regroup

hundreds as tens

tens as hundreds

tens as ones

ones as tens
Use Place Value Understandings and properties of operations to add and subtract.
When you compare numbers, you find out if a number is greater than, less than, or equal to another number. 156 > 134
Use place value to find 10 more or 10 less,100 more, or 100 less in a 3 digit number.
To find 10 more or less, look at the hundreds digit to see how it needs to change.
Hundreds 
Tens 
Ones 
4 
5 
0 
10 more
Look at the tens digit to see how it needs to change.
Hundreds 
Tens 
Ones 
4 
6 
0 
10 less
Look at the tens digit to see how it needs to change.
Hundreds 
Tens 
Ones 
4 
4 
0 
To find 100 more or less, look at the hundreds digit to see how it needs to change.
Hundreds 
Tens 
Ones 
4 
5 
0 
100 more
Look at the hundreds digit to see how it needs to change.
Hundreds 
Tens 
Ones 
5 
5 
0 
100 less
Look at the hundreds digit to see how it needs to change.
Hundreds 
Tens 
Ones 
3 
5 
0 
Place value can help you identify and extend counting patterns.
124, 125, 126, 127, 128  ones
346, 356, 366, 376, 386  tens
543, 643, 743, 843, 943  hundredsProblem Solving  Compare two 3digit numbers using the hundreds, tens, and ones digits using >, <, = symbols
Use keywords and base ten blocks to unlock the problem.

First read the problem carefully

Ask yourself 

What do I need to find?

What information do I need to use?

How will I show the information?

How will I know if I answer the question correctly?

Conor read a book with 153 pages. James read a book with 172 pages. Who read more pages?
I need to find out who read more pages.
The information I need to use is Conor read 153 pages and James read 172.
To show the information I will use blocks to show the number of pages read. First, compare the hundreds on each model. Since they are the same, compare the nens. 7 tens are greater than 5 tens, so 172 is greater than 153. So James read more pages than Conor.
I will know the answer is correct by rereading the problem to make sure I answered the question and by checking the blocks to show the values of the digits in the numbers, and then comparing them.
Use place value to compare numbers
Hundreds 
Tens 
Ones 
1 
5 
3 
1 
7 
2 
172 > 153 or 153 < 172
Add and Subtract within 20

Represent and solve problems involving addition and subtraction

Work with equal groups of objects to gain foundations for multiplication
Vocabulary
sums  answers to addition problems 4 + 3 = 7
addends  any of the numbers that are added 3 + 4 = 7
differences  the answers to subtraction problems 7  4 = 3
doubles  both addends are the same
4 + 4 = 8
addend + addend = sum
Use doubles facts to find sums for near doubles facts.
An addition fact with near doubles has an addend that is one more than the other addend.
4+5 =
If you know the sum of a doubles fact, you can find the sum for a near doubles fact by comparing the numbers being added and deciding if you need to add 1 or subtract 1 from the sum of the doubles fact.
Doubles + 1 Facts
6 + 7 =
6 and 7 are next to each other when you count, so this is a doubles + 1 fact.

Underline the smaller addend number 6 + 7 =

Double the smaller addend number 6 + 6 = 12

Add 1 to the double of the smaller addend 12 + 1 = 13
Doubles  1 Facts
6 + 7 =

Underline the larger addend number 6 + 7 =

Double the larger addend number 7 + 7 = 14

Subtract 1 from the double of the larger addend 141 = 13
Some ways to remember addition facts:

Count on 1, 2, or 3 7 + 1 = 8
7 + 2 = 9
7 + 3 = 10

When you add zero to a number, the sum is the number.
Zero plus any number equals the number. 11 + 0 = 11

Changing the order of the addends does not change the sum.
5 + 8 = 13
8 + 5 = 13

Use the make a ten strategy.
Make a Ten to Add
Break apart the lesser addend to make a ten.
8 + 5 = ? (5 = 2 + 3)
(2 + 3)
Think 8 + 2 = 10
Then add 10 plus the remaining addend to find the sum.
10 + 3 = 13
Add 3 addends

Add any two addends first, then add the third addend to that sum

Choose 2 numbers and look for the facts you know
1 + 8 + 2 = ?
1 + 10 = 11
Addition and subtraction are related.
Related addition and subtraction facts have the same whole and parts.
Use addition facts to remember differences.
They undo each other.
7 + 5 = 12 so 12  5 = 7
5 + 7 = 12 so 12  7 = 5
7 
5 
____________________12____________________
____________________12_________________________
7 
5 
Use Number lines to represent problems
A number line is a line that shows numbers in order from left to right.
l___________l
12  5 = 7
2+3
12  2 = 10
10  3 = 7

Getting to 10 in subtraction helps to find a difference.

When you get to 10 you can use a tens fact to find the difference.
Subtract 53  7=? in two steps.
Break 7 into 3 and 4
Next, subtract the 3 from 53. 533=50
Finally, subtract the remaining 4 ones 504=46
When you break apart a number, you can subtract some of the ones to get to a ten number and then subtract the remaining ones to find the difference .
Use Drawings to Represent Problems
Use bar models to show the parts and the whole that you know to help find what is missing.
larger amount 
smaller amount 
? 
difference
13  6 = 7
13 
6 
7 (difference) 
Use Equations to Represent Problems

A number sentence can be used to show a problem

A number sentence has an operation symbol (+ or ) and an equal sign (=).
This is a horizontal number sentence: 4 + 6 = 10
This is a vertical number sentence 7
+3
10
A is a placeholder for a missing number.
There were some boys and 5 girls at the park. There were 13 children in all. How many boys were at the park? + 5 = 13
There were 9 chocolate chip cookies and 7 oatmeal cookies on the plate. How many cookies were there altogether? 9 + 7 =
There were 15 crayons in the box. Tom took 4 crayons out. How many were left? 15  4 =
Use keywords to identify the operation in word problems
When you add, you join two or more smaller groups together to get a larger number. *** + *****
3 + 5 = 8
ADD When you see these words
how many altogether total sum in all plus
When you subtract, you start with the larger number and find out how many are left or which group has more. When you take away, you end up with a smaller number. 12  4 = 8
SUBTRACT when you see these words 