5th Grade Math · Parent guide
What Math Should a 5th Grader Know?
Complete Parent Guide
By the end of 5th grade, your child should add and subtract fractions with different denominators (like 2/3 + 1/4), multiply fractions and mixed numbers, divide a unit fraction by a whole number and a whole number by a unit fraction, add, subtract, multiply and divide decimals to hundredths, multiply multi-digit numbers with the standard method, divide by two-digit numbers, find the volume of rectangular boxes, and graph points on a coordinate grid. The Common Core names three focus areas for grade 5: fraction operations, decimals and multi-digit division, and volume.
Reviewed against the Common Core standards.
What 5th Graders Learn in Math, by Domain
These are the Common Core State Standards for Grade 5 math, grouped by domain and put into plain English. Many states use them as written or in an adapted version, so your school's wording may differ slightly. The code after each skill is the standard it comes from, and each domain links to the full text on the Common Core site. Read the official Grade 5 introduction.
Operations & Algebraic Thinking
Common Core 5.OA- Use parentheses, brackets and braces in expressions and evaluate them (5.OA.1)
- Write expressions from words, such as "add 8 and 7, then multiply by 2" as 2 × (8 + 7) (5.OA.2)
- Build two number patterns from two rules and graph the pairs (5.OA.3)
Number & Operations in Base Ten
Common Core 5.NBT- Know that each place is 10 times the place to its right and 1/10 of the place to its left (5.NBT.1)
- Explain patterns when multiplying or dividing by 10, 100 and 1000, and use exponents for powers of 10 (5.NBT.2)
- Read, write, compare and round decimals to thousandths (5.NBT.3, 5.NBT.4)
- Multiply multi-digit whole numbers fluently with the standard algorithm (5.NBT.5)
- Divide up to four-digit numbers by two-digit numbers (5.NBT.6)
- Add, subtract, multiply and divide decimals to hundredths (5.NBT.7)
Number & Operations: Fractions
Common Core 5.NF- Add and subtract fractions and mixed numbers with unlike denominators (5.NF.1)
- Understand a fraction as division: 3/4 is 3 ÷ 4 (5.NF.3)
- Multiply a fraction or whole number by a fraction, and find the area of rectangles with fraction sides (5.NF.4)
- Predict the size of a product: multiplying by a fraction less than 1 makes a number smaller (5.NF.5)
- Divide a unit fraction by a whole number and a whole number by a unit fraction, such as 4 ÷ 1/5 = 20 (5.NF.7)
Measurement & Data
Common Core 5.MD- Convert units within one system, such as 5 cm to 0.05 m, in multi-step problems (5.MD.1)
- Make line plots of fractional measurements and solve problems with them (5.MD.2)
- Understand volume as unit cubes and use V = l × w × h and V = b × h for rectangular prisms (5.MD.3-5.MD.5)
- Find the volume of a shape made of two rectangular prisms by adding (5.MD.5)
Geometry
Common Core 5.G- Graph points in the first quadrant of the coordinate plane and explain what they mean in a real situation (5.G.1, 5.G.2)
- Classify shapes in a hierarchy: every square is a rectangle, so every square has four right angles (5.G.3, 5.G.4)
What 5th Grade Math Problems Look Like
Original practice problems written to match the standards above, with the answer and the thinking we would hope to hear.
Unlike denominators (5.NF.1)
Ana walked 2/3 of a mile to the park and 1/4 of a mile to the store. How far did she walk?
Answer: 11/12 of a mile. 2/3 = 8/12 and 1/4 = 3/12, and 8/12 + 3/12 = 11/12.
Dividing with unit fractions (5.NF.7)
How many 1/3-cup servings are in 2 cups of raisins?
Answer: 6 servings. Each cup holds 3 servings, so 2 ÷ 1/3 = 6.
Decimals (5.NBT.7)
A notebook costs $2.35. How much do 4 notebooks cost?
Answer: $9.40. 4 × 2 = 8, 4 × 0.35 = 1.40, and 8 + 1.40 = 9.40.
Volume of a combined shape (5.MD.5)
A box is made of two parts: one is 4 in × 3 in × 2 in and the other is 2 in × 3 in × 5 in. What is the total volume?
Answer: 54 cubic inches. 24 + 30 = 54.
Signs Your 5th Grader May Be Behind in Math
Fifth grade fraction and decimal work is what 6th grade ratios and 7th grade equations are built on. Watch for these:
- !Adds tops and bottoms: writes 1/2 + 1/3 = 2/5
- !Is surprised that 1/2 × 8 is smaller than 8, because "multiplying makes bigger"
- !Lines up decimals by the last digit, so 3.2 + 1.45 comes out as 1.77
- !Cannot estimate whether 47 into 1,316 is about 20 or about 30 when dividing by a two-digit number
- !Mixes up volume and area, or adds the three edge lengths instead of multiplying
Short At-Home Activities (10 Minutes or Less)
Cook with fractions
Double or halve a recipe. "The recipe needs 3/4 cup of milk and we are making half. How much?" That is 1/2 × 3/4 = 3/8, a 5th grade standard in one question.
Estimate before every answer
Ask "about how much?" before your child computes. 2/3 + 1/4 should be a bit less than 1, so 3/7 is clearly wrong.
Receipt math
Hand over a receipt and ask for the total of three items, or how much change from $20. Decimals to hundredths are 5th grade work.
Build boxes
Use dice, sugar cubes or building bricks to build a 3 × 2 × 4 box and count the cubes, then show that 3 × 2 × 4 gives the same 24.
Coordinate treasure hunt
Draw a grid on paper, hide a "treasure" at (4, 7) and give clues. Remind your child: across first, then up.
Find Your Child's Exact Level
Fifth grade is the bridge to middle school math. Our diagnostic checks fraction and decimal operations, division and volume and shows you which 5th grade skills need work, in about 10 minutes.
Start the DiagnosticQuestions Parents Ask
What is the most important math skill in 5th grade?
Fraction operations. The first focus area the Common Core names for grade 5 is fluency with adding and subtracting fractions, plus understanding how to multiply fractions and divide in limited cases. Sixth grade ratios and 7th grade equations assume this.
Do 5th graders divide fractions?
Only in two simple cases: a unit fraction divided by a whole number (1/3 ÷ 4) and a whole number divided by a unit fraction (4 ÷ 1/5) (5.NF.7). Dividing any fraction by any fraction, like 2/3 ÷ 3/4, is a 6th grade standard.
Should my 5th grader be able to do long division with two-digit divisors?
Yes. The standard asks 5th graders to divide up to four-digit numbers by two-digit numbers, using place value strategies and explaining with equations, arrays or area models (5.NBT.6). Fluency with the standard division algorithm is listed in 6th grade (6.NS.2).
My child gets the right answer but cannot explain it. Does that matter?
It matters more in 5th grade than before. Several standards ask students to explain why a method works, such as why multiplying by a fraction less than 1 gives a smaller answer (5.NF.5). Children who only memorize steps often stall when fractions get mixed with decimals and equations.
What is order of operations in 5th grade?
Fifth graders evaluate expressions with parentheses, brackets and braces (5.OA.1) and write expressions from words. The formal order of operations with exponents comes up again in 6th grade (6.EE.2).