Third grade math

Third grade is the hinge year. Multiplication facts to 10 by 10 need to become automatic, and fractions arrive properly for the first time. TEKS wants fractions with denominators of 2, 3, 4, 6, and 8 built on the number line, not just as pizza slices, plus place value to 100,000, area and perimeter, elapsed time, scaled graphs, and a personal financial literacy strand that Common Core does not have. If facts do not become quick this year, everything after it gets harder. Our rooms cover this grade more thoroughly than any other. The gap is personal financial literacy, which we have nothing for.

• K
• 1st
• 2nd
• 3rd
• 4th
• 5th

What to aim for this year

By the end of third grade, a child working at grade level can usually do these.

• Composes and decomposes numbers up to 100,000 using expanded notation
• Compares and orders whole numbers to 100,000
• Recalls multiplication facts up to 10 by 10 automatically, and the matching division facts
• Multiplies a two-digit number by a one-digit number using the standard algorithm
• Represents fractions with denominators of 2, 3, 4, 6, and 8 using objects, strip diagrams, and number lines
• Explains that the unit fraction one over b is one part of a whole cut into b equal parts
• Explains why two fractions are equivalent using the number line or a same-size whole
• Determines the area of a rectangle by multiplying, and finds perimeter
• Tells and writes time to the nearest minute and determines elapsed time
• Summarizes data with frequency tables, dot plots, and bar graphs with scaled intervals
• Explains the connection between work and income, and gives reasons to save (TEKS financial literacy)
• Tells polygons apart from other figures by their straight sides and closed outline
• Names the shapes in the quadrilateral family and says what each one requires
• Finds area by covering a figure with same-size unit squares and counting them
• Finds the area of an L-shaped figure by breaking it into rectangles and adding
• Shows that rectangles with the same perimeter can have very different areas
• Finds an unknown side length of a rectangle when the perimeter is already known
• Sorts two-dimensional figures using a rule such as number of sides or square corners
• Represents an addition or subtraction problem with a strip diagram, one of the pictorial models Texas expects in third grade
• Labels the unknown on a strip diagram so the picture shows which operation to use
• Recognizes a two-step problem and works out which step has to happen first
• Finds the hidden middle question inside a two-step word problem
• Represents a multiplication problem with a strip diagram of equal boxes
• Tells apart the two kinds of division problems, sharing into a set number of groups and making groups of a set size
• Checks an answer against the story to see whether it could really have happened
• Shows that a number on a number line sits between two tens in a row
• Shows that a number sits between two hundreds in a row and tells which one it is nearer
• Rounds a whole number to the nearest ten
• Rounds a whole number to the nearest hundred
• Uses rounding to estimate a sum and to judge whether an answer is reasonable
• Shows halves, fourths, and eighths as distances from zero on a number line and names the fraction at a marked point
• Builds a dot plot on an evenly spaced number line, including the values where nothing landed
• Measures lengths to the nearest half inch and plots them on a line plot marked in halves
• Reads a scaled pictograph where one symbol stands for several things, including half symbols
• Solves one-step and two-step problems using data shown in a dot plot or frequency table
• Decides which questions a given graph can and cannot answer
• Explains how scarce something is changes what it costs (TEKS 3.9B financial literacy)
• Names the cost and the benefit of planned spending and of unplanned spending (TEKS 3.9C financial literacy)
• Explains that credit is used when a need or want costs more than you can pay right now, and that paying it back is the borrower's job (TEKS 3.9D financial literacy)
• Gives reasons to save and explains why a savings plan for something far off, like college, works (TEKS 3.9E financial literacy)
• Works through one day that involves income, spending, saving, credit and giving all at once (TEKS 3.9F financial literacy)
• Compares two fractions that share a top number or a bottom number and shows the answer with the greater than, less than, and equal signs
• Recognizes that a fraction whose top number equals its bottom number is one whole

Teach it here

These rooms teach it on this site. No sign-up, nothing to buy, and they work with the internet switched off. Start here. Everything below is a fallback for when you want more than the app gives you.

• build — Sticks and corners on a pegboard: naming a shape by how many sides it has, cutting one shape into two, putting smaller shapes together to make a bigger one, the four-sided family, folding a shape in half, and checking a corner against a square one.
• zipline — The number line: reading its scale, naming the number at a marked point, distance between two points, subtracting by counting up, rounding, estimation, zooming in to hundredths, and whole numbers, fractions and decimals as places on one line.
• plot — Sorting a pile into a table and then making the dot plot of it, reading answers back off the dots, halves on a line plot, stem-and-leaf, and a first scatterplot.
• times — Multiplication facts to 10 by 10
• share — Division as fair sharing and the facts that pair with multiplication
• frac — Cutting a whole into equal parts, naming the shaded fraction, and seeing that a fraction like four fourths is one whole
• measure — Area and perimeter of rectangles
• factors — Factor pairs sitting behind the times tables
• column — Two-digit by one-digit multiplication and multi-digit addition
• money — Money problems in context
• graph — Scaled bar graphs, dot plots, and frequency tables, and deciding which questions a chart can answer at all and which it cannot.
• clock — Time to the minute and elapsed time
• units — Measurement units and sensible tool choice
• bonds — Number relationships that keep mental math quick
• bar — Strip diagrams: marking the unknown and choosing add or take away from where it sits, building a strip of equal boxes for a times story, the two kinds of division, and judging whether someone's answer could really have happened.
• place — Big numbers to 100,000: pulling them apart into expanded notation and putting them back together, comparing and ordering them, and rounding to estimate a sum and check whether an answer makes sense.
• volume — Holding area, perimeter and volume side by side: yards with the same fence and different room inside, a missing side worked back from the fence, boxes filled with unit cubes a layer at a time, floor times height, two boxes added together, and choosing which of the three a real job needs with the right label.
• wallet — Pay per job times jobs worked, reasons to save, how scarcity moves a price, the cost and benefit of planned and unplanned buys, credit as borrowing with interest, and one whole day of income, spending, saving, giving and buying on credit.

What a week looks like

1. Five days, about 40 minutes, with the first five minutes always on multiplication facts.
2. Three days on the current topic, one day on fractions no matter what else is happening, one review day.
3. Run /times daily until the facts are automatic. Daily beats long.
4. Do one multi-step word problem a day and make him draw it before he calculates.
5. Once a week, measure something real: a room, a board, a recipe.

If you want more, free

A fallback, not the plan. Every one of these costs nothing, and the license tag says what you may actually DO with it, which is a different question from whether it is free to read.

• MEP Primary, Year 4 (CIMT) Free Free to use

  Complete lesson plans and practice books, with a strong multiplication and division sequence and problem sets noticeably harder than typical American third grade work. This is the free spine our family defaults to.

  License: Free to download, copyright retained by the originators through CIMT, non-profit-making purposes only.

• Illustrative Mathematics K-5 Math, Grade 3 Free CC BY

  Free through Kendall Hunt. The fraction units stand out because they build fractions on the number line from the start, which is what the standards actually ask for and what a lot of programs handle poorly.

  License: CC BY 4.0. Openly licensed, adapt and share with attribution.

• Simply Good and Beautiful Math 3 (The Good and the Beautiful) Free Openly licensed

  120 parent-led lessons, free as a PDF. Gentler and more colorful than MEP, with games built in. General Christian worldview throughout.

  License: Free to download and use, copyright retained by the publisher. Not openly licensed.

• Khan Academy, 3rd grade math Free CC BY-NC-SA Not confirmed

  Genuinely useful this year for multiplication fact practice and for re-teaching a specific fraction idea that did not land. The immediate feedback suits drill better than it suits first instruction.

  License: Free to use. Terms of Service state CC BY-NC-SA 4.0 for Licensed Educational Content; video licensing has reportedly changed. Check before adapting.

• EngageNY Mathematics, Grade 3 modules Free CC BY-NC-SA

  The Grade 3 fraction and multiplication modules are carefully sequenced from concrete to abstract and hold up well against paid programs. Free PDFs, heavy on printing. Download from the New York State archive.

  License: CC BY-NC-SA. Free for non-commercial use with attribution and ShareAlike. Eureka Math Squared is a separate paid product.

And the paid programs, honestly

Nothing here is required. These are the programs families most often ask about, with the real drawback of each one named rather than skipped.

• Beast Academy Level 3 Paid About $100 per year online, verified at $99.99, or roughly $120 to $130 for a full printed level.

  Good at: Deep conceptual and problem-solving material. The guide comics teach mathematical thinking, and the practice problems are puzzles rather than exercises.

  Drawback: It will not build fact fluency for you, and third grade is exactly the year fluency matters most, so you must run drill separately. Children who need reassurance rather than challenge often find it punishing.

  Suits: A confident child who already has his facts, or one paired with a separate drill program.

• Math-U-See Gamma Paid Roughly $130 to $145 for a Level Up Set with blocks already owned, or about $220 for a complete set.

  Good at: Multiplication taught to genuine mastery, with the blocks making the array structure visible. A child who cannot get his facts often gets them here.

  Drawback: A whole year on one operation, with very little geometry, measurement, data, or fraction work, all of which third grade standards require. You will need to supplement those strands yourself.

  Suits: A child who has hit a wall on multiplication facts and needs one thing at a time.

• Dimensions Math 3 (Singapore Math Inc.) Paid $14.50 per book, about $58 for student books, meaningfully more with guides.

  Good at: Bar modeling comes into its own here and is a strong tool for multi-step word problems. The problems are well constructed and build in real steps.

  Drawback: The Home Instructor's Guide is necessary and adds cost. Bar modeling is unfamiliar to most American parents, so there is a real learning curve on your side before you can teach it.

  Suits: A parent willing to learn the method first, teaching a child who can already multiply.

• Saxon Math 3 Paid Roughly $150 to $235 for the home study kit depending on retailer, heavily discounted from list. Manipulatives separate.

  Good at: Continuous review keeps multiplication facts and earlier arithmetic alive all year, which is the exact failure point in third grade. Very predictable daily structure.

  Drawback: Conceptual development is thin, particularly on fractions, and the lessons are long and dry. Saxon's numbering gets confusing after this level, since Math 5/4 follows Math 3.

  Suits: A child whose facts decay without constant revisiting, in a household that wants a fixed routine.

• Math Mammoth Grade 3 (Light Blue Series) Paid About $40 as a download, frequently discounted, and cheaper in a bundle.

  Good at: Mastery-based with clear conceptual explanations, and inexpensive. Covers the full breadth of the standards rather than a single topic, unlike some mastery competitors.

  Drawback: Visually plain and worksheet-heavy, and the pages can run long enough to discourage a slow writer. You will be printing a lot.

  Suits: A family wanting full standards coverage on a small budget, with a child who works independently.

Prices are approximate and change often. Check with the publisher before you buy. We describe and link to these programs; none of their material is hosted here.

The rest of third grade