Grade 5 math
Lessons commonly taught in grade 5, each with worked examples, practice problems, and complete solutions. Topics often span more than one grade, so you may see a lesson listed under a neighboring grade too.
23 lessons · 57 standards
Whole Numbers & Operations
- Long Division: The Standard Algorithm
How to divide multi-digit numbers by long division, what each of the four repeating steps is doing, how to handle a remainder, and how to check the answer.
- Multi-Digit Multiplication: The Standard Algorithm
How to multiply multi-digit numbers with the standard algorithm, why the second row is shifted one place left, and how to check an answer by estimating first.
- Numerical Patterns and Graphing Ordered Pairs
How to generate a number pattern from a rule, spot the relationship between two patterns, form ordered pairs from them, and graph those pairs in the first quadrant.
- Order of Operations: Why 2 + 3 × 4 Is 14
The order operations are carried out in, why multiplication comes before addition, how parentheses override the order, and how to work through a long expression safely.
Fractions
- Adding Fractions With Unlike Denominators
How to add fractions with different bottom numbers: find a common denominator, rewrite both fractions, add the top numbers, then simplify. With mixed numbers too.
- Dividing Fractions: Keep, Change, Flip — and Why
How to divide fractions by multiplying by the reciprocal, why flipping the second fraction works, and how to divide with whole numbers and mixed numbers.
- Fraction Word Problems: Choosing the Right Operation
How to decide whether a fraction word problem needs addition, subtraction, multiplication or division, with the signal words and worked solutions for each.
- Converting Fractions to Decimals and Back
Two ways to turn a fraction into a decimal, how to tell in advance whether it will terminate or repeat, and how to convert a decimal back into a fraction.
- Least Common Denominator: Finding a Shared Bottom Number
How to find the least common denominator of two fractions using multiples, prime factors, or the multiply-the-bottoms shortcut, and why you need one.
- Mixed Numbers and Improper Fractions: Converting Both Ways
How to change an improper fraction into a mixed number by dividing, how to change it back by multiplying, and when each form is the useful one.
- Multiplying Fractions: Top Times Top, Bottom Times Bottom
How to multiply fractions and mixed numbers, why the rule works using an area model, why the product can be smaller than what you started with, and how to cancel first.
- Simplifying Fractions: Reducing to Lowest Terms
How to simplify a fraction by dividing top and bottom by a common factor, how to use the GCF to do it in one step, and how to know when you are done.
- Subtracting Fractions: Like and Unlike Denominators
How to subtract fractions with the same or different bottom numbers, and how to borrow when the fraction you are taking away is bigger than the one you have.
Decimals
- Adding and Subtracting Decimals
How to add and subtract decimals by lining up the decimal points, why the alignment matters, and how to handle numbers with different lengths.
- Comparing and Ordering Decimals
How to compare decimals by working left to right one place at a time, why a longer decimal is not automatically bigger, and how to put a list in order.
- Decimal Place Value: Reading and Writing Decimals
What each place after the decimal point is worth, how to read a decimal aloud, and how to write one in expanded form or as a fraction.
- Dividing Decimals: Move the Point, Then Divide
How to divide by a decimal by shifting both numbers until the divisor is whole, why that shift is allowed, and how to divide a decimal by a whole number.
- Multiplying Decimals: Count the Decimal Places
How to multiply decimals by ignoring the points, multiplying as whole numbers, then counting the decimal places — and why that count is what it is.
- Rounding Decimals to Any Place
How to round a decimal to the nearest whole, tenth or hundredth: find the place, look at the digit after it, and decide whether to round up or keep it.
Measurement & Data
- Converting Measurement Units
How to convert between units in the same system, when to multiply and when to divide, and how to use a conversion inside a multi-step problem.
Statistics and Probability
- Line Plots with Fractions
How to build a line plot from measurements in halves, quarters and eighths, how to read one, and how to use it to answer questions about totals and redistribution.
Geometry
- Classifying Quadrilaterals: The Shape Hierarchy
How quadrilaterals are sorted by their properties, why every square is a rectangle, and how a shape inherits every attribute of the categories it belongs to.
- Volume of a Rectangular Prism: Length × Width × Height
Why the volume of a box is length times width times height, why the units are cubed, and how the base-times-height form works for any prism.
Standards covered
- CCSS.MATH.CONTENT.4.MD.A.1
- CCSS.MATH.CONTENT.4.MD.B.4
- CCSS.MATH.CONTENT.4.NBT.B.5
- CCSS.MATH.CONTENT.4.NBT.B.6
- CCSS.MATH.CONTENT.4.NF.A.1
- CCSS.MATH.CONTENT.4.NF.B.3
- CCSS.MATH.CONTENT.4.NF.B.3a
- CCSS.MATH.CONTENT.4.NF.B.3b
- CCSS.MATH.CONTENT.4.NF.B.3c
- CCSS.MATH.CONTENT.4.NF.B.4
- CCSS.MATH.CONTENT.4.NF.C.6
- CCSS.MATH.CONTENT.4.NF.C.7
- CCSS.MATH.CONTENT.4.OA.C.5
- CCSS.MATH.CONTENT.5.G.A.2
- CCSS.MATH.CONTENT.5.G.B.3
- CCSS.MATH.CONTENT.5.G.B.4
- CCSS.MATH.CONTENT.5.MD.A.1
- CCSS.MATH.CONTENT.5.MD.B.2
- CCSS.MATH.CONTENT.5.MD.C.3
- CCSS.MATH.CONTENT.5.MD.C.3a
- CCSS.MATH.CONTENT.5.MD.C.3b
- CCSS.MATH.CONTENT.5.MD.C.4
- CCSS.MATH.CONTENT.5.MD.C.5
- CCSS.MATH.CONTENT.5.MD.C.5a
- CCSS.MATH.CONTENT.5.MD.C.5b
- CCSS.MATH.CONTENT.5.MD.C.5c
- CCSS.MATH.CONTENT.5.NBT.A.1
- CCSS.MATH.CONTENT.5.NBT.A.2
- CCSS.MATH.CONTENT.5.NBT.A.3
- CCSS.MATH.CONTENT.5.NBT.A.3a
- CCSS.MATH.CONTENT.5.NBT.A.3b
- CCSS.MATH.CONTENT.5.NBT.A.4
- CCSS.MATH.CONTENT.5.NBT.B.5
- CCSS.MATH.CONTENT.5.NBT.B.6
- CCSS.MATH.CONTENT.5.NBT.B.7
- CCSS.MATH.CONTENT.5.NF.A.1
- CCSS.MATH.CONTENT.5.NF.A.2
- CCSS.MATH.CONTENT.5.NF.B.3
- CCSS.MATH.CONTENT.5.NF.B.4
- CCSS.MATH.CONTENT.5.NF.B.4a
- CCSS.MATH.CONTENT.5.NF.B.4b
- CCSS.MATH.CONTENT.5.NF.B.5
- CCSS.MATH.CONTENT.5.NF.B.5a
- CCSS.MATH.CONTENT.5.NF.B.5b
- CCSS.MATH.CONTENT.5.NF.B.6
- CCSS.MATH.CONTENT.5.NF.B.7
- CCSS.MATH.CONTENT.5.NF.B.7a
- CCSS.MATH.CONTENT.5.NF.B.7b
- CCSS.MATH.CONTENT.5.NF.B.7c
- CCSS.MATH.CONTENT.5.OA.A.1
- CCSS.MATH.CONTENT.5.OA.A.2
- CCSS.MATH.CONTENT.5.OA.B.3
- CCSS.MATH.CONTENT.6.NS.A.1
- CCSS.MATH.CONTENT.6.NS.B.2
- CCSS.MATH.CONTENT.6.NS.B.3
- CCSS.MATH.CONTENT.6.NS.B.4
- CCSS.MATH.CONTENT.7.NS.A.2d