Focus Areas for Fourth Grade
- Developing understanding of multi-digit multiplication
- Developing understanding of fraction equivalence and operations
- Understanding geometric figures and their properties
- Working with decimals and measurement conversion
Math Standards by Domain
Operations and Algebraic Thinking (4.OA)
What Students Learn:
Students learn to interpret multiplication as a comparison (e.g., "a red hat costs 3 times as much as a blue hat") and solve multi-step word problems using all four operations. They understand the relationships between multiplication and division and can represent these problems with equations that include unknowns.
Key Skills:
- Interpret multiplication equations as comparisons (e.g., 35 = 5 x 7 means 35 is 5 times as many as 7)
- Multiply or divide to solve word problems involving multiplicative comparison
- Solve multi-step word problems using addition, subtraction, multiplication, and division
- Represent problems using equations with a letter standing for the unknown quantity
- Assess reasonableness of answers using mental computation and estimation
- Use mental math to check solutions
A blue ribbon is 4 inches long. A red ribbon is 3 times as long. How long is the red ribbon? (4 x 3 = 12 inches)
Example (Multi-Step):A bakery made 48 muffins. They sold 15 in the morning and put the rest into boxes of 6. How many boxes did they fill? (48 - 15 = 33, then 33 ÷ 6 = 5 boxes with 3 left over)
What Students Learn:
Students explore the structure of whole numbers by finding all factor pairs for numbers 1-100 and determining whether numbers are prime or composite. They also generate and analyze patterns following given rules, which develops algebraic thinking and helps them identify relationships between numbers.
Key Skills:
- Find all factor pairs for whole numbers 1-100 (e.g., 24: 1x24, 2x12, 3x8, 4x6)
- Recognize that a whole number is a multiple of each of its factors
- Determine whether a number (1-100) is prime or composite
- Identify prime numbers: numbers with exactly two factors (1 and itself)
- Identify composite numbers: numbers with more than two factors
- Generate number or shape patterns following a given rule
- Identify and explain features of patterns (e.g., all numbers in the pattern are even)
Factor pairs of 36: 1x36, 2x18, 3x12, 4x9, 6x6
36 is composite (has more than 2 factors); 37 is prime (only 1x37)
Example (Patterns):Rule: Start with 3, add 4 each time → 3, 7, 11, 15, 19, 23...
Feature: All numbers in this pattern are odd
Number and Operations in Base Ten (4.NBT)
What Students Learn:
Students extend their place value understanding to include multi-digit whole numbers up to 1,000,000. They recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right. This deep understanding of place value is crucial for all operations with large numbers.
Key Skills:
- Recognize that in a multi-digit number, each place is 10 times the place to its right
- Understand place value relationships: 5 in the thousands place is 10 times larger than 5 in the hundreds place
- Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form
- Compare two multi-digit numbers based on place value using >, =, and < symbols
- Round multi-digit whole numbers to any place (tens, hundreds, thousands, etc.)
- Use place value understanding to explain rounding decisions
In 555,555, each 5 represents a different value: 500,000 + 50,000 + 5,000 + 500 + 50 + 5
The 5 in the ten-thousands place (50,000) is 10 times the 5 in the thousands place (5,000)
Example (Rounding):Round 3,742 to the nearest hundred: Look at tens place (4). Since 4 < 5, round down to 3,700
Round 867,521 to the nearest thousand: Look at hundreds (5). Since 5 ≥ 5, round up to 868,000
What Students Learn:
Students develop fluency with adding and subtracting multi-digit numbers (up to 1,000,000) using the standard algorithm. They understand how the algorithm works based on place value and properties of operations, including when and how to regroup (carry or borrow) across multiple places.
Key Skills:
- Fluently add multi-digit whole numbers using the standard algorithm
- Fluently subtract multi-digit whole numbers using the standard algorithm
- Understand regrouping (carrying) in addition across multiple places
- Understand regrouping (borrowing) in subtraction across zeros and multiple places
- Check addition using subtraction and vice versa
- Apply place value understanding to explain why the algorithm works
- Solve real-world problems involving large numbers
45,678 + 37,845 = 83,523
Add ones (8+5=13, write 3 carry 1), tens (7+4+1=12, write 2 carry 1), hundreds (6+8+1=15, write 5 carry 1), etc.
Example (Subtraction across zeros):50,000 - 23,456 = 26,544
Regroup from ten-thousands: 50,000 becomes 4 ten-thousands, 10 thousands, which becomes 9 thousands, 10 hundreds, etc.
What Students Learn:
Students learn to multiply larger numbers using strategies based on place value and properties of operations. This includes multiplying up to a 4-digit number by a 1-digit number (like 2,456 x 7) and two 2-digit numbers (like 43 x 28). They use methods such as area models, partial products, and the standard algorithm.
Key Skills:
- Multiply up to 4-digit by 1-digit numbers (e.g., 3,456 x 8)
- Multiply two 2-digit numbers (e.g., 47 x 23)
- Use strategies based on place value: break numbers into place values and multiply separately
- Use properties of operations: distributive property, associative property
- Use area models and arrays to visualize multiplication
- Apply the standard multiplication algorithm with understanding
- Estimate products to check reasonableness of answers
2,456 x 7 = (2,000 x 7) + (400 x 7) + (50 x 7) + (6 x 7) = 14,000 + 2,800 + 350 + 42 = 17,192
Example (2-digit x 2-digit):34 x 26 using partial products:
30 x 20 = 600
30 x 6 = 180
4 x 20 = 80
4 x 6 = 24
Total: 600 + 180 + 80 + 24 = 884
What Students Learn:
Students learn to divide multi-digit numbers by one-digit divisors, understanding that division can result in a quotient with a remainder. They use strategies based on place value, properties of operations, and the relationship between multiplication and division. They learn to interpret remainders in the context of word problems.
Key Skills:
- Divide up to 4-digit dividends by 1-digit divisors (e.g., 2,456 ÷ 7)
- Find whole-number quotients and remainders
- Use strategies based on place value and properties of operations
- Use the relationship between multiplication and division to check work
- Apply equations and area models to represent and solve division problems
- Interpret remainders in context (round up, round down, or express as a fraction)
- Estimate quotients to check reasonableness
2,456 ÷ 7 = ?
7 goes into 24 three times (3 x 7 = 21), remainder 3
Bring down 5 to make 35. 7 goes into 35 five times (5 x 7 = 35), remainder 0
Bring down 6. 7 goes into 6 zero times, remainder 6
Answer: 350 R 6 or 350 with 6 left over
Check: (350 x 7) + 6 = 2,450 + 6 = 2,456 ✓
Example (Interpreting remainders):125 students go on a field trip. Each bus holds 30 students. How many buses are needed? 125 ÷ 30 = 4 R 5, so we need 5 buses (round up to fit everyone)
Number and Operations—Fractions (4.NF)
What Students Learn:
Students develop a deep understanding of fraction equivalence by recognizing that two fractions are equivalent if they represent the same size or the same point on a number line. They learn to generate equivalent fractions by multiplying or dividing the numerator and denominator by the same number, and to compare fractions with different numerators and denominators.
Key Skills:
- Explain why two fractions are equivalent using visual models (area models, number lines)
- Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4 = 3/6)
- Understand that multiplying numerator and denominator by the same number creates an equivalent fraction
- Compare two fractions with different numerators and denominators using >, =, < symbols
- Compare fractions by creating common denominators or common numerators
- Use benchmark fractions (0, 1/2, 1) to reason about fraction size
- Justify comparisons using visual models and reasoning about size
1/3 = 2/6 = 3/9 = 4/12
Explain: If I multiply both parts of 1/3 by 2, I get 2/6. The pieces are smaller but there are more of them, so the total amount is the same.
Example (Comparing):Compare 3/4 and 2/3:
Make common denominator of 12: 3/4 = 9/12 and 2/3 = 8/12
Since 9/12 > 8/12, then 3/4 > 2/3
What Students Learn:
Students learn that fractions are built from unit fractions (fractions with numerator 1). They add and subtract fractions with the same denominator by combining unit fractions, and they learn to multiply a fraction by a whole number. They also solve word problems involving addition, subtraction, and multiplication of fractions.
Key Skills:
- Understand a fraction a/b as a sum of unit fractions 1/b (e.g., 3/4 = 1/4 + 1/4 + 1/4)
- Add fractions with like denominators (e.g., 2/8 + 3/8 = 5/8)
- Subtract fractions with like denominators (e.g., 5/6 - 2/6 = 3/6 = 1/2)
- Add and subtract mixed numbers with like denominators
- Solve word problems involving addition and subtraction of fractions
- Multiply a fraction by a whole number (e.g., 3 x 2/5 = 6/5 = 1 1/5)
- Solve word problems involving multiplication of fractions by whole numbers
- Understand and apply decomposition of fractions
3/8 + 2/8 = 5/8 (three-eighths plus two-eighths equals five-eighths)
1 2/5 + 3/5 = 1 5/5 = 2 (mixed number addition)
Example (Multiplying Fraction by Whole Number):4 x 3/10 = 12/10 = 1 2/10 = 1 1/5
Word problem: Each lap around the track is 1/4 mile. If you run 5 laps, how far did you run? 5 x 1/4 = 5/4 = 1 1/4 miles
What Students Learn:
Students are introduced to decimal notation as another way to represent fractions, specifically fractions with denominators of 10 or 100. They learn to convert between fraction and decimal forms, understand that decimals are an extension of the place value system, and compare decimal numbers to the hundredths place.
Key Skills:
- Express fractions with denominator 10 as decimals (e.g., 7/10 = 0.7)
- Express fractions with denominator 100 as decimals (e.g., 43/100 = 0.43)
- Understand that tenths can be written as hundredths (e.g., 0.3 = 0.30 = 30/100)
- Use decimal notation to express fractions (e.g., 68/100 = 0.68)
- Compare two decimals to hundredths using >, =, < symbols
- Understand place value of decimals: tenths place, hundredths place
- Recognize equivalent decimals (e.g., 0.5 = 0.50)
3/10 = 0.3 (three-tenths)
47/100 = 0.47 (forty-seven hundredths)
6/10 = 60/100 = 0.60 = 0.6
Example (Comparing Decimals):Compare 0.7 and 0.65:
0.7 = 0.70 = 70/100 and 0.65 = 65/100
Since 70/100 > 65/100, then 0.7 > 0.65
Measurement and Data (4.MD)
What Students Learn:
Students develop a deeper understanding of measurement by learning the relative sizes of different measurement units and converting between them. They apply formulas for area and perimeter of rectangles to solve real-world problems. This includes understanding relationships between units in both customary and metric systems.
Key Skills:
- Know relative sizes of measurement units: 1 ft = 12 in, 1 yd = 3 ft, 1 mile = 5,280 ft
- Know metric relationships: 1 km = 1,000 m, 1 m = 100 cm, 1 cm = 10 mm
- Convert larger units to smaller units (e.g., 5 feet = 60 inches)
- Convert measurements within a single system (customary or metric)
- Apply the area formula A = l x w for rectangles
- Apply the perimeter formula P = 2l + 2w for rectangles
- Solve real-world problems involving area, perimeter, distance, time, volume, mass, and money
- Use the four operations to solve measurement word problems
How many inches are in 4 feet? 4 x 12 = 48 inches
How many centimeters are in 3.5 meters? 3.5 x 100 = 350 cm
Example (Area and Perimeter):A rectangular garden is 12 feet long and 8 feet wide.
Area: A = 12 x 8 = 96 square feet
Perimeter: P = (2 x 12) + (2 x 8) = 24 + 16 = 40 feet
What Students Learn:
Students learn to create and interpret line plots that display measurement data in fractions of a unit (halves, fourths, eighths). This combines their understanding of fractions with data representation, and they solve problems by adding and subtracting fractions based on information in the line plots.
Key Skills:
- Make line plots to display data sets of measurements in fractions of a unit (1/2, 1/4, 1/8)
- Interpret line plots showing fractional measurements
- Solve problems involving addition and subtraction of fractions using information from line plots
- Determine differences between data points on a line plot
- Find total amounts by adding fractions shown on line plots
- Analyze and describe patterns in fractional measurement data
Measure the lengths of 10 pencils to the nearest 1/4 inch:
Results: 5 1/4 in (2 pencils), 5 1/2 in (3 pencils), 5 3/4 in (4 pencils), 6 in (1 pencil)
Create line plot with X marks above each measurement on number line
Questions to solve:
- What is the difference between the longest and shortest pencil? 6 - 5 1/4 = 3/4 inch
- What is the combined length of the two shortest pencils? 5 1/4 + 5 1/4 = 10 2/4 = 10 1/2 inches
What Students Learn:
Students are introduced to angles and angle measurement. They learn that an angle is formed by two rays sharing a common endpoint and that angle measurement is additive (adjacent angles can be added together). They use protractors to measure angles and solve problems involving angle measures.
Key Skills:
- Recognize angles as geometric shapes formed by two rays with a common endpoint
- Understand that angles are measured in degrees
- Know that a full rotation is 360°, half rotation is 180°, quarter rotation is 90°
- Measure angles in whole-number degrees using a protractor
- Sketch angles of specified measure (e.g., sketch a 45° angle)
- Understand angle measure is additive: when an angle is decomposed into non-overlapping parts, the angle measure is the sum of the measures of the parts
- Solve addition and subtraction problems to find unknown angles
Right angle: 90°
Acute angle: less than 90° (e.g., 45°, 60°)
Obtuse angle: greater than 90° but less than 180° (e.g., 120°, 150°)
Straight angle: 180°
Example (Additive Angles):A large angle measures 120°. It's divided into two smaller angles. One measures 70°. What is the measure of the other angle?
120° - 70° = 50°
Geometry (4.G)
What Students Learn:
Students develop precision in geometric vocabulary and concepts. They learn to identify and draw basic geometric elements including points, lines, line segments, rays, angles, and special relationships like perpendicular and parallel lines. They also classify two-dimensional figures based on the presence or absence of these elements.
Key Skills:
- Draw and identify points, lines, line segments, and rays
- Draw and identify angles: right, acute, obtuse
- Identify perpendicular lines (lines that form right angles)
- Identify parallel lines (lines in the same plane that never intersect)
- Classify two-dimensional figures based on presence or absence of parallel or perpendicular lines
- Classify figures based on presence or absence of specific angle types
- Use proper geometric notation and vocabulary
Point: An exact location in space (labeled with a capital letter: Point A)
Line: Extends infinitely in both directions (notation: line AB or AB with arrows)
Line segment: Part of a line with two endpoints (notation: segment AB or AB with bars)
Ray: Part of a line with one endpoint, extends infinitely in one direction
Example (Classification):Rectangle: Has 4 right angles, 2 pairs of parallel sides, 2 pairs of perpendicular sides
Trapezoid: Has exactly 1 pair of parallel sides
What Students Learn:
Students learn to classify and identify two-dimensional shapes based on their specific attributes. They explore symmetry by recognizing line-symmetric figures (shapes that can be folded along a line so both halves match exactly) and by drawing lines of symmetry. This deepens their understanding of shape properties and relationships.
Key Skills:
- Classify triangles by angles: acute (all angles < 90°), right (one 90° angle), obtuse (one angle > 90°)
- Classify triangles by sides: equilateral (all sides equal), isosceles (2 sides equal), scalene (no sides equal)
- Classify quadrilaterals: square, rectangle, rhombus, parallelogram, trapezoid
- Recognize line-symmetric figures (figures with at least one line of symmetry)
- Draw lines of symmetry in two-dimensional figures
- Identify that some figures have multiple lines of symmetry (e.g., square has 4)
- Understand that some shapes have no lines of symmetry
A triangle with angles 60°, 60°, 60° is: equilateral (all sides equal) and acute (all angles < 90°)
A triangle with angles 90°, 45°, 45° is: isosceles (2 sides equal) and right (has 90° angle)
Example (Symmetry):Square: 4 lines of symmetry (2 diagonal, 2 through midpoints of opposite sides)
Rectangle: 2 lines of symmetry (through midpoints of opposite sides)
Regular pentagon: 5 lines of symmetry
Scalene triangle: 0 lines of symmetry