Focus Areas for First Grade
- Developing understanding of addition and subtraction
- Understanding whole number relationships and place value
- Developing understanding of linear measurement
- Reasoning about shapes and their attributes
Math Standards by Domain
Operations and Algebraic Thinking (1.OA)
What Students Learn:
Students learn to solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, and to solve problems involving adding to, taking from, putting together, taking apart, and comparing.
Key Skills:
- Solve addition and subtraction word problems within 20
- Use objects, drawings, and equations with a symbol for the unknown number
- Add three whole numbers whose sum is 20 or less
Sam has 8 apples. His friend gives him 5 more. How many apples does Sam have now? (8 + 5 = ?)
What Students Learn:
Students apply properties like the commutative and associative properties of addition. They understand that subtraction can be thought of as an unknown-addend problem (e.g., 10 - 6 = ? is the same as 6 + ? = 10).
Key Skills:
- Understand and apply commutative property: 5 + 3 = 3 + 5
- Understand and apply associative property: 2 + 6 + 4 = 2 + 10
- Relate subtraction to missing addend problems
If 9 - 4 = ?, think: "4 + ? = 9" (Answer: 5)
What Students Learn:
Students develop fluency with addition and subtraction within 20. They learn various strategies including counting on, making ten, decomposing numbers, and using the relationship between addition and subtraction.
Key Skills:
- Count forward when adding (start at 8, count on 5 more)
- Count backward when subtracting
- Fluently add and subtract within 10
- Use strategies like "make ten" (7 + 5 = 7 + 3 + 2 = 10 + 2)
To solve 8 + 6, students might think: "8 + 2 = 10, and 4 more makes 14"
What Students Learn:
Students learn that the equal sign means "the same as" and can find missing numbers in various positions in equations (e.g., 8 = ? - 5, not just 8 + 5 = ?).
Key Skills:
- Understand that = means both sides have the same value
- Determine true or false: 5 = 5 (true), 7 = 8 - 1 (true)
- Find the unknown in different positions: 5 + ? = 12, ? + 3 = 11, 8 - ? = 5
Find the missing number: 6 + _ = 15 (Answer: 9, because 6 + 9 = 15)
Number and Operations in Base Ten (1.NBT)
What Students Learn:
Students extend their counting skills beyond 100 to 120. They practice starting at any number (not just 1) and counting forward. They also learn to read and write numbers up to 120 and represent quantities with the appropriate numeral.
Key Skills:
- Count forward from any number less than 120 to 120
- Read numbers up to 120 (e.g., recognize "117" as one hundred seventeen)
- Write numbers up to 120 in standard form
- Represent a set of objects (like 115 blocks) with the correct numeral
- Understand the pattern in counting (100, 101, 102...)
Start counting at 97 and count forward: 97, 98, 99, 100, 101, 102, 103...
If there are 114 pencils, students write the numeral "114"
What Students Learn:
Students develop a foundational understanding of place value by recognizing that two-digit numbers are composed of tens and ones. For example, 45 is 4 tens and 5 ones. They learn to compare numbers based on their place values using comparison symbols.
Key Skills:
- Understand that 10 ones equals 1 ten
- Decompose numbers: 67 = 6 tens + 7 ones = 60 + 7
- Compare two-digit numbers based on tens first, then ones
- Use symbols correctly: > (greater than), < (less than), = (equal to)
- Explain why 58 > 52 (5 tens = 5 tens, but 8 ones > 2 ones)
Compare 34 and 39: 34 < 39 (both have 3 tens, but 4 ones < 9 ones)
What is 73? It's 7 tens and 3 ones, or 70 + 3
What Students Learn:
Students apply their understanding of place value to perform addition and subtraction. They learn mental math strategies like finding 10 more or 10 less by adding or subtracting from the tens place, and they practice subtracting multiples of 10.
Key Skills:
- Add within 100 using place value understanding and properties of operations
- Mentally calculate 10 more than a number (e.g., 10 more than 47 is 57)
- Mentally calculate 10 less than a number (e.g., 10 less than 62 is 52)
- Subtract multiples of 10 (e.g., 70 - 30 = 40)
- Use concrete models or drawings to explain reasoning
10 more than 38: Think "3 tens and 8 ones → 4 tens and 8 ones = 48"
60 - 20: Think "6 tens - 2 tens = 4 tens = 40"
35 + 23: Think "3 tens + 2 tens = 5 tens, 5 ones + 3 ones = 8 ones = 58"
Measurement and Data (1.MD)
What Students Learn:
Students begin to understand measurement by comparing lengths of objects. They learn to order objects from shortest to longest and to measure lengths using non-standard units (like paper clips or blocks) and standard units. This is their introduction to linear measurement concepts.
Key Skills:
- Compare three objects and order them by length (shortest to longest)
- Use indirect comparison (if A is longer than B, and B is longer than C, then A is longer than C)
- Express length as a whole number of length units
- Measure objects using non-standard units (e.g., "the book is 8 paper clips long")
- Understand that measuring means laying units end-to-end with no gaps or overlaps
Order by length: A pencil (15 cm), a crayon (9 cm), and a marker (12 cm)
Answer: crayon < marker < pencil
The pencil is 6 paper clips long (place paper clips end-to-end along the pencil)
What Students Learn:
Students learn to tell time to the hour and half-hour on both analog (with hands) and digital clocks. They understand that the short hand points to the hour and the long hand points to the minutes, and they can write the time in standard notation.
Key Skills:
- Identify the hour hand (short) and minute hand (long) on analog clocks
- Tell time to the hour (e.g., 3:00, when minute hand is on 12)
- Tell time to the half-hour (e.g., 3:30, when minute hand is on 6)
- Read digital clocks showing hours and half-hours
- Write time in standard format (3:00, 7:30)
- Understand that 30 minutes = half an hour
Analog clock: Hour hand between 4 and 5, minute hand on 6 → 4:30
Digital clock showing 9:00 → "nine o'clock"
What time is it? Hour hand on 2, minute hand on 12 → 2:00 or "two o'clock"
What Students Learn:
Students learn to collect, organize, and display data using simple charts and graphs. They practice asking and answering questions about the data, including finding totals and comparing categories. This introduces basic data analysis skills.
Key Skills:
- Organize data into up to three categories
- Represent data using tables, tally charts, and picture graphs
- Interpret data by answering questions about it
- Compare categories (which has more? which has fewer?)
- Find the total number of data points
- Draw conclusions from simple data displays
Survey: What's your favorite fruit?
Apples: 5 students, Bananas: 8 students, Oranges: 4 students
Questions: Which fruit is most popular? (Bananas) How many students chose apples or oranges? (5 + 4 = 9) How many more students chose bananas than oranges? (8 - 4 = 4)
Geometry (1.G)
What Students Learn:
Students learn to identify the essential characteristics that define a shape (like the number of sides and angles) versus attributes that don't define the shape (like color, size, or orientation). They understand that a triangle is always a triangle regardless of its size or color.
Key Skills:
- Identify defining attributes: number of sides, number of angles/corners, closed vs. open
- Recognize non-defining attributes: color, size, orientation (turned different ways)
- Understand that a triangle always has 3 sides and 3 corners, no matter what it looks like
- Build and draw shapes given specific defining attributes
- Explain why a shape is or isn't a particular geometric figure
Defining attributes of a rectangle: 4 sides, 4 right angles, opposite sides equal
Non-defining attributes: whether it's red or blue, large or small, horizontal or vertical
All of these are triangles even though they look different: △ ▲ ◭
What Students Learn:
Students learn to combine simple shapes to create more complex shapes and to break apart complex shapes into simpler components. This develops spatial reasoning and understanding of how shapes relate to each other. It's like building with geometric blocks.
Key Skills:
- Combine two or more shapes to make a new shape (e.g., two triangles make a square)
- Compose both 2D shapes (flat) and 3D shapes (solid)
- Decompose shapes into smaller parts
- Create pictures or designs using multiple shapes
- Recognize that shapes can be built using other shapes
- Use pattern blocks or tangrams to explore shape composition
Put two triangles together to make a square or rectangle
A hexagon can be made from 6 triangles or 3 rhombuses
Stack cubes to build a tower or rectangular prism
Decompose: A house shape can be broken into a square (walls) and a triangle (roof)
What Students Learn:
Students learn to divide circles and rectangles into equal parts (halves and fourths/quarters). This is an introduction to fractions, helping them understand that shapes can be divided into equal-sized pieces and introducing vocabulary like "half" and "fourth" or "quarter."
Key Skills:
- Partition (divide) circles into 2 equal shares (halves)
- Partition circles into 4 equal shares (fourths or quarters)
- Partition rectangles into 2 equal shares (halves)
- Partition rectangles into 4 equal shares (fourths or quarters)
- Use vocabulary: halves, fourths, quarters, half of, fourth of, quarter of
- Understand that equal shares must be the same size
- Recognize that a whole can be divided into multiple equal parts
Cut a pizza (circle) in half: Draw 1 line through the center = 2 equal pieces
Cut a pizza into fourths: Draw 2 lines through the center = 4 equal pieces
Divide a rectangular brownie into 4 equal parts (quarters)
Each person gets one-half or one-fourth of the whole shape