Focus Areas for Second Grade
- Extending understanding of base-ten notation
- Building fluency with addition and subtraction
- Using standard units of measure
- Describing and analyzing shapes
Math Standards by Domain
Operations and Algebraic Thinking (2.OA)
What Students Learn:
Students extend their problem-solving skills to larger numbers (within 100) and tackle more complex problems that require two steps. They work with various problem types including adding to, taking from, putting together, taking apart, and comparing quantities.
Key Skills:
- Solve one-step word problems with addition and subtraction within 100
- Solve two-step word problems (e.g., first add, then subtract)
- Understand different problem situations: joining, separating, comparing
- Represent problems using equations with unknowns in various positions
- Use drawings, objects, and equations to model problems
- Check if answers make sense in context
Maria has 45 stickers. She gives 18 to her friend. How many does she have left? (45 - 18 = 27)
Example (Two-Step):Carlos had 30 marbles. He won 15 more, then lost 8. How many does he have now? (30 + 15 = 45, then 45 - 8 = 37)
What Students Learn:
Students develop fluency and automaticity with basic addition and subtraction facts. By the end of second grade, they should know all basic addition facts (0+0 through 9+9) from memory and be able to quickly find related subtraction facts.
Key Skills:
- Fluently (quickly and accurately) add and subtract within 20
- Memorize all sums of two one-digit numbers (addition facts 0-9)
- Use mental strategies: making ten, doubles, near doubles
- Derive subtraction facts from known addition facts (if 7+8=15, then 15-8=7)
- Use strategies like counting on, counting back, and fact families
- Build speed and accuracy through practice
Making 10: 8 + 7 = (8 + 2) + 5 = 10 + 5 = 15
Doubles: 6 + 6 = 12
Near Doubles: 6 + 7 = (6 + 6) + 1 = 13
Fact Families: 9 + 4 = 13, so 13 - 4 = 9
What Students Learn:
Students learn to identify odd and even numbers by pairing objects or using skip-counting by 2s. They understand that even numbers can be divided into two equal groups with no leftovers, while odd numbers have one object left over.
Key Skills:
- Determine if a number (up to 20) is odd or even
- Pair objects to check: even numbers pair perfectly, odd numbers have one left over
- Write equations showing even numbers as sums of equal addends (12 = 6 + 6)
- Recognize patterns: numbers ending in 0, 2, 4, 6, 8 are even
- Recognize patterns: numbers ending in 1, 3, 5, 7, 9 are odd
- Skip count by 2s to identify even numbers
Is 14 even or odd? 14 = 7 + 7 (two equal groups), so 14 is even
Is 15 even or odd? 15 = 7 + 7 + 1 (can't make equal pairs), so 15 is odd
Make pairs with 18 counters: ●● ●● ●● ●● ●● ●● ●● ●● ●● (9 pairs, no leftovers = even)
What Students Learn:
Students are introduced to the foundation of multiplication through rectangular arrays. They learn to count objects arranged in rows and columns using repeated addition, which builds the foundation for understanding multiplication in third grade.
Key Skills:
- Identify rows and columns in a rectangular array
- Count total objects in arrays (up to 5×5)
- Write repeated addition equations for arrays (3 rows of 4: 4 + 4 + 4 = 12)
- Understand that arrays can be counted by rows or by columns
- Draw arrays to represent situations
- Build foundation for understanding multiplication
Array with 3 rows and 4 columns:
●●●● (row 1)
●●●● (row 2)
●●●● (row 3)
By rows: 4 + 4 + 4 = 12 (3 groups of 4)
By columns: 3 + 3 + 3 + 3 = 12 (4 groups of 3)
Number and Operations in Base Ten (2.NBT)
What Students Learn:
Students extend their place value understanding to three-digit numbers (hundreds, tens, ones). They learn to count to 1000, skip-count by 5s, 10s, and 100s, read and write large numbers in different forms, and compare three-digit numbers.
Key Skills:
- Understand 3-digit numbers: 256 = 2 hundreds + 5 tens + 6 ones = 200 + 50 + 6
- Count within 1000, starting from any number
- Skip-count by 5s: 5, 10, 15, 20...
- Skip-count by 10s: 10, 20, 30, 40...
- Skip-count by 100s: 100, 200, 300, 400...
- Read and write numbers to 1000 in standard form (456), word form (four hundred fifty-six), and expanded form (400 + 50 + 6)
- Compare three-digit numbers using >, =, < based on place value
What is 372? 3 hundreds + 7 tens + 2 ones = 300 + 70 + 2
Compare: 456 > 419 (both have 4 hundreds, but 5 tens > 1 ten)
Skip-count by 5s from 85: 85, 90, 95, 100, 105...
Write 508 in words: five hundred eight
What Students Learn:
Students develop fluency with two-digit addition and subtraction within 100 using various strategies based on place value and properties of operations. They also learn to add multiple two-digit numbers efficiently.
Key Skills:
- Fluently add two-digit numbers within 100 (e.g., 47 + 38)
- Fluently subtract two-digit numbers within 100 (e.g., 82 - 35)
- Use mental strategies and algorithms
- Add up to four two-digit numbers (e.g., 23 + 15 + 31 + 18)
- Use place value: add tens to tens, ones to ones
- Apply strategies like compensation, breaking apart numbers, using friendly numbers
47 + 38 = (40 + 30) + (7 + 8) = 70 + 15 = 85
82 - 35 = (80 - 30) + (2 - 5) = 50 + (-3) = 47 (or use regrouping)
Add four numbers: 23 + 15 + 31 + 18 = (23 + 31) + (15 + 18) = 54 + 33 = 87
What Students Learn:
Students extend their addition and subtraction skills to three-digit numbers within 1000. They develop mental math strategies for adding or subtracting 10 or 100 from any number and learn to explain why their strategies work.
Key Skills:
- Add three-digit numbers within 1000 using concrete models, drawings, or strategies
- Subtract three-digit numbers within 1000
- Mentally add 10 or 100 to numbers 100-900 (e.g., 367 + 10 = 377)
- Mentally subtract 10 or 100 from numbers 100-900 (e.g., 542 - 100 = 442)
- Explain and justify addition and subtraction strategies using place value
- Understand relationships between digits in different places
456 + 237: Add hundreds (400+200=600), tens (50+30=80), ones (6+7=13), then combine: 600+80+13=693
Mental math: 543 + 100 = 643 (add 1 hundred to the hundreds place)
Mental math: 378 - 10 = 368 (subtract 1 ten from the tens place)
Explain: "I added hundreds to hundreds, tens to tens, and ones to ones, then combined the results."
Measurement and Data (2.MD)
What Students Learn:
Students transition from non-standard units to standard units of measurement. They learn to measure objects using rulers and measuring tools, estimate lengths, and understand the relationship between different units of measurement.
Key Skills:
- Measure length using standard units: inches, feet, centimeters, meters
- Select appropriate tools for measuring (ruler, meter stick, measuring tape)
- Estimate lengths before measuring
- Understand that longer units need fewer iterations (fewer meters than centimeters)
- Measure twice using different units and describe the relationship
- Compare lengths of different objects using standard units
Measure a pencil: about 7 inches or about 18 centimeters
Estimate before measuring: "I think the desk is about 3 feet long." Measure: "It's 4 feet long."
The same desk is 48 inches or 4 feet (we need more inches because they're smaller)
What Students Learn:
Students connect measurement to addition and subtraction by solving problems involving lengths. They use number line diagrams to represent and solve these problems, understanding that lengths can be added and subtracted just like other numbers.
Key Skills:
- Solve word problems involving lengths using addition (e.g., total length of two objects)
- Solve word problems involving lengths using subtraction (e.g., how much longer is one object than another?)
- Use number line diagrams to represent addition and subtraction of lengths
- Work with lengths in the same unit
- Write equations to represent length problems
A ribbon is 35 cm long. Another ribbon is 28 cm long. How long are they together? 35 + 28 = 63 cm
Maria's plant is 42 inches tall. Tom's plant is 37 inches tall. How much taller is Maria's plant? 42 - 37 = 5 inches
Number line: Show 25 + 15 by starting at 25 and jumping forward 15 to land on 40
What Students Learn:
Students extend their time-telling skills to five-minute intervals and learn about a.m. and p.m. They also work with money, counting coins and bills, and solving practical word problems involving money.
Key Skills:
- Tell time to the nearest 5 minutes on analog clocks (3:15, 3:20, 3:25)
- Write time using digital notation and understand a.m. (morning) and p.m. (afternoon/evening)
- Identify and know the value of coins: penny (1¢), nickel (5¢), dime (10¢), quarter (25¢)
- Count collections of coins to find their total value
- Solve word problems involving money using $ and ¢ symbols
- Use addition and subtraction to solve money problems
Clock shows hour hand between 7 and 8, minute hand on 6 → 7:30 a.m. (if morning)
Example (Money):Count: 2 quarters + 3 dimes + 1 nickel = 25¢ + 25¢ + 10¢ + 10¢ + 10¢ + 5¢ = 85¢
Problem: A pencil costs 35¢. You pay with 50¢. How much change? 50¢ - 35¢ = 15¢
What Students Learn:
Students learn to collect measurement data and create different types of graphs to display it. They work with line plots (for measurement data), picture graphs, and bar graphs, and answer questions by interpreting the data.
Key Skills:
- Measure objects to create a data set (e.g., measure lengths of different pencils)
- Create line plots showing measurement data in whole number units
- Draw picture graphs where each picture represents one or more objects
- Draw single-unit bar graphs to represent data sets with up to 4 categories
- Answer questions based on the graphs (how many, how many more, etc.)
- Compare categories and find totals from graphs
Measure 10 crayons, record lengths: 3 in, 3 in, 4 in, 3 in, 4 in, 4 in, 5 in, 4 in, 3 in, 5 in
Create line plot with X marks above 3, 4, and 5 inches
Example (Bar Graph):Favorite pets: Dogs (7), Cats (5), Fish (3), Birds (2)
Draw bars for each category, answer: "How many more chose dogs than fish?" (7-3=4)
Geometry (2.G)
What Students Learn:
Students learn to identify shapes based on their specific attributes (number of sides, angles, faces) rather than just by appearance. They learn to draw shapes with given characteristics and identify shapes like pentagons, hexagons, cubes, and more based on their defining features.
Key Skills:
- Recognize and name shapes by their attributes: triangle (3 sides), quadrilateral (4 sides), pentagon (5 sides), hexagon (6 sides)
- Identify 3D shapes: cubes, cones, cylinders, spheres, rectangular prisms
- Draw 2D shapes with specified number of sides or angles
- Identify shapes that have specific attributes (e.g., "Find all shapes with 4 sides")
- Understand that shapes in different orientations and sizes can be the same shape
- Recognize that some shapes have equal sides/faces and some don't
Draw a shape with 5 sides → pentagon
Which shapes have exactly 3 sides? All triangles
Identify: A cube has 6 square faces, all equal
Draw a quadrilateral (any 4-sided shape: square, rectangle, trapezoid, rhombus)
What Students Learn:
Students learn to divide rectangles into equal-sized squares arranged in rows and columns. This builds understanding of arrays and area, and lays groundwork for multiplication. They practice counting the total number of squares in different ways.
Key Skills:
- Partition (divide) rectangles into rows and columns of same-size squares
- Identify the number of rows and columns in a partitioned rectangle
- Count the total number of squares by counting all, counting by rows, or counting by columns
- Understand that all squares must be the same size
- Create different partitions of the same rectangle
- Build foundation for understanding area and multiplication
Partition a rectangle into 3 rows and 4 columns of squares
How many squares total? Count by rows: 4 + 4 + 4 = 12, or count by columns: 3 + 3 + 3 + 3 = 12
A rectangle can be divided into 2 rows of 5 squares = 10 squares total
What Students Learn:
Students extend their fraction understanding from Grade 1 by learning to partition shapes into halves, thirds, and fourths. They learn fraction vocabulary and understand that equal shares of identical wholes don't have to look the same (e.g., a circle can be cut into fourths vertically or with two perpendicular lines).
Key Skills:
- Partition circles into 2, 3, or 4 equal shares (halves, thirds, fourths)
- Partition rectangles into 2, 3, or 4 equal shares
- Use vocabulary: halves, thirds, half of, third of, fourth of, quarter of
- Recognize that equal shares of the same whole don't have to be the same shape
- Understand that more equal shares means smaller pieces
- Describe the whole as 2 halves, 3 thirds, or 4 fourths
Partition a circle into thirds: Draw 2 lines from center creating 3 equal pie pieces
Partition a rectangle into fourths: Can divide it 2 ways horizontally and vertically, or 4 ways horizontally, or 4 ways vertically
Compare: A fourth is smaller than a half (when divided into more pieces, each piece is smaller)
The whole circle = 4 fourths (or 4 quarters)