The big picture for third grade
Most of what follows comes from the Common Core State Standards for grade 3. Some states use their own standards, which may word things differently or move a skill by a year, so your child's teacher is the best guide to what their class follows. The standards name four areas that matter most in grade 3:
- Multiplication and division within 100: what they mean, and strategies for working them out.
- Fractions, especially unit fractions such as 1/3 and 1/8, where the top number is 1.
- Area, and how a rectangle covered in rows of squares connects to multiplication.
- Flat shapes: sorting and describing them by their sides and angles.
Alongside those, third graders round numbers, add and subtract within 1,000, tell time to the minute, measure in liters, grams and kilograms, and read and draw bar graphs. That is a lot for one year, which is why third grade can feel like a jump.
Multiplication and division
This is the heart of the year. Third graders learn what multiplication means before they learn the facts by heart: 5 × 7 is 5 groups of 7, or an array of 5 rows with 7 in each row. Division is the same idea run backwards. 56 ÷ 8 can mean sharing 56 things into 8 equal groups (how many in each?) or putting 56 things into groups of 8 (how many groups?). By the end of grade 3, children are expected to:
- Know from memory all products of two one-digit numbers, such as 6 × 7 = 42 and 8 × 9 = 72.
- Multiply and divide fluently within 100, using the link between the two: if 6 × 8 = 48, then 48 ÷ 8 = 6.
- Find a missing number in a fact, such as 8 × ? = 48.
- Multiply a one-digit number by a multiple of 10, such as 9 × 80 = 720.
- Solve two-step word problems using all four operations, and check whether the answer is reasonable by estimating.
Children don't need the formal names for properties like commutative or distributive, but they use the ideas all the time: 3 × 8 is the same as 8 × 3, and 7 × 6 can be split into 5 × 6 plus 2 × 6, which is 30 + 12 = 42.
Rounding and adding within 1,000
Third graders round whole numbers to the nearest 10 or 100: 347 rounds to 350 to the nearest 10, and to 300 to the nearest 100. Rounding is how children check whether an answer makes sense. A child who adds 412 + 389 and writes 11 in the ones place, instead of regrouping, gets 7,911. An estimate of 400 + 400 = 800 shows at once that something went wrong. The correct answer is 801.
Children also learn to add and subtract within 1,000 fluently, using place value. Subtracting across zeros, as in 503 - 278, is a classic sticking point: the ones need regrouping but there are no tens to regroup from, so the child has to start with the hundreds. The answer is 225.
Fractions as numbers
Grade 3 is where fractions properly begin. A unit fraction such as 1/4 is one part when a whole is cut into 4 equal parts, and 3/4 is three of those parts. The word equal matters: a sandwich cut into one big piece and one small piece has not been cut into halves.
- Fractions on a number line. To find 1/4, split the space from 0 to 1 into 4 equal parts. The first mark is 1/4, and three jumps of 1/4 from 0 land on 3/4.
- Simple equivalent fractions, such as 1/2 = 2/4 and 2/3 = 4/6, explained with a picture or a number line rather than a rule.
- Whole numbers as fractions: 3 = 3/1, and 4/4 = 1.
- Comparing fractions with the same denominator (3/8 is less than 5/8) or the same numerator (3/4 is more than 3/6), as long as both are parts of the same-sized whole.
In grade 3 the denominators are kept to 2, 3, 4, 6 and 8, and adding fractions comes later. A practice guide on teaching fractions from the US Institute of Education Sciences recommends number lines as a central tool from the early grades, because they show that a fraction is a number with its own size, not just a slice of pizza.
Area and perimeter
Area is how much flat space a shape covers, measured by counting unit squares that fit inside it with no gaps or overlaps. Third graders start by tiling and counting, then notice the shortcut: a rectangle 4 squares wide and 6 squares long holds 4 rows of 6, so its area is 4 × 6 = 24 square units.
They also meet perimeter, the distance all the way around a shape. A favorite task shows how different the two are: rectangles of 1 by 5, 2 by 4 and 3 by 3 all have a perimeter of 12 units, but their areas are 5, 8 and 9 square units. If your child mixes them up, ask: "Are we covering it, or going around it?"
Time, measurement, graphs and shapes
- Time to the nearest minute on an analog clock, and elapsed time in minutes. If soccer practice starts at 3:45 and lasts 50 minutes, it ends at 4:35.
- Liquid volume and mass in liters, grams and kilograms, including estimating: is a bag of apples closer to 1 kilogram or 10?
- Picture graphs and bar graphs where one picture or square stands for more than one thing, such as 5 pets, with "how many more" and "how many fewer" questions.
- Measuring lengths to the nearest half or quarter inch, and showing the results on a line plot.
- Sorting shapes by their sides and angles. A square is also a rectangle and a rhombus, and all three are quadrilaterals.
Signs your child may need some help
These are things worth noticing, not a checklist for a diagnosis. One wobble means little, especially early in the year. A pattern that lasts several weeks is worth a conversation with the teacher.
- By spring, still counting up from the start of a table for facts like 6 × 7, or using fingers for every fact.
- Cannot say what 4 × 3 means or draw it as groups or an array, even when they know the answer is 12.
- Treats 42 ÷ 7 as a brand-new fact, with no link to 6 × 7.
- Thinks 1/8 is bigger than 1/4 because 8 is bigger than 4, or calls any piece of a shape "a half".
- Calls 3:45 "4:45" because the hour hand is close to the 4.
- Gives the perimeter when asked for the area, again and again.
- Avoids word problems, or homework that should take 15 minutes regularly ends in tears.
If you see a pattern, look one step back. Trouble with division is often trouble with multiplication facts, and trouble with multiplication is often trouble with skip counting or the idea of equal groups. Take two or three pieces of recent work to the teacher and ask which skills are not secure yet and what would help most at home.
If difficulties continue for months despite good teaching and steady practice, ask the school about extra support. In the US, federal special education law (IDEA) lets a parent request an initial evaluation, and once you give consent it must be completed within 60 days or within your state's own timeframe. Put the request in writing.
Simple activities at home
Ten minutes with everyday things often does more than another worksheet, because your child can see and touch the math. Pick one activity at a time.
- Arrays in the kitchen. A muffin tin or an egg carton is an array. How many cups in 3 rows of 4? Turn it around: is 4 rows of 3 the same?
- Snack sharing. Share 24 crackers equally among 4 people (24 ÷ 4 = 6 each), then ask what fraction of the crackers each person got (1/4).
- Fact triangles. Write 6, 7 and 42 on a card and ask for all four facts: 6 × 7, 7 × 6, 42 ÷ 6 and 42 ÷ 7.
- Paper-strip fractions. Fold strips into halves, quarters and eighths and line them up, then mark the same fractions on a number line from 0 to 1.
- Measure a room. Count floor tiles, or lay out sticky notes, to find the area of a rug. Then walk around its edge with a tape measure for the perimeter.
- Clock questions. Keep an analog clock in view. "It's 4:20 and dinner is at 5:00. How many minutes is that?"
- Estimate at the store. $38 and $47 round to $40 and $50, so the total is about $90. Then check the exact total, $85.
Keep practice short and calm
Little and often works best: 10 minutes on most days beats an hour on the weekend. Start with something your child can already do, spend most of the time on one skill, and stop while it is still going well. Ask them to explain how they got an answer, right or wrong. "I did 5 × 6 and added two more 6s" tells you far more than the answer alone.
Eurekami's free 3rd grade math pages take each grade 3 skill in turn, with a worked example, practice questions and printable worksheets, and there are free topic pages for times tables, telling time, area and perimeter, rounding and fractions. In the app, Daily Practice starts with a placement test that steps back to find the real missing skill. Whatever you use, the order is the same: understanding first, then the facts, then speed.
