Fourth grade math

Fourth grade is the arithmetic heavy lifting: two-digit by two-digit multiplication, long division with a one-digit divisor, and decimals to hundredths tied back to fractions. Fractions with equal denominators get added and subtracted, and equivalence gets formalized. Geometry picks up too, with angle measurement using a protractor and classification by parallel and perpendicular lines. TEKS adds a financial literacy strand covering profit and fixed versus variable expenses. Our rooms cover multiplication, division, fractions, place value, measurement, and multi-step problems. Angles and protractor work, and the financial literacy strand, each have a room of their own now. A real protractor on real paper is still a weekly job for the table.

• K
• 1st
• 2nd
• 3rd
• 4th
• 5th

What to aim for this year

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

• Represents decimals to tenths and hundredths with models, money, and number lines, and relates them to fractions
• Compares and orders decimals to the hundredths
• Adds and subtracts whole numbers and decimals to the hundredths using the standard algorithm
• Multiplies a two-digit number by a two-digit number using the standard algorithm, and models it with arrays or area
• Divides up to a four-digit dividend by a one-digit divisor
• Adds and subtracts fractions with equal denominators using objects and pictorial models
• Determines equivalent fractions and compares fractions with different numerators and denominators
• Classifies two-dimensional figures by parallel and perpendicular lines and by angle size, and identifies lines of symmetry
• Measures and draws angles with a protractor
• Converts measurements within the customary system and within the metric system
• Represents data in frequency tables, dot plots, and stem-and-leaf plots
• Calculates profit and distinguishes fixed from variable expenses (TEKS financial literacy)
• Identifies points, lines, line segments, and rays and tells them apart
• Classifies angles as acute, right, obtuse, or straight by their measure in degrees
• Understands an angle measure as a fraction of a full turn around a circle
• Adds and subtracts angle measures to find an unknown angle
• Classifies triangles as right, acute, or obtuse based on their angles
• Finds and draws every line of symmetry in a two-dimensional figure
• Tells prisms and pyramids apart and counts the faces, edges, and vertices of each
• Writes an equation with a letter standing for the unknown, which Texas expects in fourth grade
• Solves multiplicative comparison problems, where one amount is a number of times another
• Tells the difference between adding a difference and multiplying by a number of times
• Plans the order of steps in a multi-step problem before computing anything
• Interprets the remainder in a division word problem instead of just reporting it
• Decides when a remainder means one more group is needed
• Names the decimal to the tenths place that matches a marked point on a number line
• Names the decimal to the hundredths place at a point by zooming in between two tenths
• Rounds whole numbers to a given place value through the hundred thousands
• Rounds by looking at the digit just to the right of the place being rounded
• Uses rounding to estimate a real total and judge whether an answer makes sense
• Reads a stem-and-leaf plot to find how many values there are, the smallest, and the largest
• Measures to the nearest eighth of an inch and shows the fractions on a line plot
• Adds and subtracts fractions using the measurements shown on a line plot
• Describes the shape of a dot plot using clusters, gaps and outliers
• Solves two-step problems from a dot plot by multiplying each value by its count and then adding
• Sorts a household's expenses into fixed and variable, and knows which ones can actually be cut (TEKS 4.10A financial literacy)
• Compares places to keep savings and names an advantage and a drawback of each (TEKS 4.10C financial literacy)
• Divides a weekly allowance among spending, saving and sharing before any of it is spent (TEKS 4.10D financial literacy)
• Describes the basic purpose of a bank or credit union: keeping money safe, lending it, and letting people borrow (TEKS 4.10E financial literacy)
• Explains the difference between working a job for pay and owning a business that keeps whatever is left after costs
• Compares decimals to the hundredths and writes the answer using the greater than, less than, and equal signs
• Reads and writes fractions greater than one, where the top number is larger than the bottom number
• Renames a fraction greater than one as a whole number plus a fraction, which is called a mixed number
• Rewrites a mixed number as a single fraction whose top number is larger than its bottom number
• Adds mixed numbers whose fractions have the same bottom number, trading extra pieces for a 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.

• point — Decimals, with the multiplying stages built round the only part anybody gets wrong: the digits are done for him and the question is where the point lands. Reading and ordering to thousandths, comparing hundredths with <, > and =, rounding, multiplying and dividing, and turning a fraction into a decimal by dividing.
• box — Solid shapes he can turn over in his head: naming a sphere, cylinder, cone and cube, matching each to a real thing in the house, sorting by what rolls and what stacks, counting faces, edges and corners, telling a prism from a pyramid, and picking the flat net that folds up into it.
• 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 making the dot plot of it, reading answers back off the dots, halves on a line plot, the shape of a dot plot (cluster, gap, outlier), and two-step totals: each length times its count, then add.
• times — Multi-digit multiplication practice
• share — Division, including long division steps
• frac — Equal and compared fractions, adding like pieces, fractions greater than one, mixed numbers both ways, adding mixed numbers by trading pieces for a whole, and adding and subtracting lengths read off a line plot
• place — Rounding to any place through the hundred thousands by the digit just to its right, estimating real totals to check an answer, and place value extended into decimals
• column — Standard algorithms for multiplication and subtraction
• measure — Area, perimeter, and unit conversion
• factors — Factor pairs, useful for simplifying fractions
• units — Converting within customary and metric systems
• graph — Frequency tables and dot plots
• clock — Elapsed time in multi-step problems
• treasure — Multi-step problem solving practice
• bar — Times as many against more than, writing the equation with a letter for the unknown, and planning both steps of a two-step problem before doing any arithmetic.
• angles — Angles measured in degrees: telling points, lines, segments and rays apart, acute, right, obtuse and straight by the number, an angle as a slice of a 360-degree turn, reading a drawn protractor on both rows of numbers and turning it to line up a tilted angle, turning the arm to make an angle, adding and subtracting angles to find a missing one, triangles sorted by their angles, and drawing every line of symmetry in a shape.
• wallet — Giving every dollar of an allowance a job before spending, sorting household bills into fixed and variable from three months of amounts, the profit on a small stand after its costs, and what a bank, a credit union and a check-cashing place do differently.

What a week looks like

1. Five days, 45 to 50 minutes, split into two sittings if attention runs out.
2. Open with a five-minute mixed fact review. Facts still decay at this age.
3. Two days on the computation topic, two on fractions or decimals, one on geometry or measurement.
4. Protractor work needs a real protractor and real paper. Do it once a week.
5. End the week with one hard multi-step problem and let him struggle with it before you help.

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 5 (CIMT) Free Free to use

  Full lesson plans and practice books covering the fourth grade range and beyond, and notably demanding on multi-step reasoning. It uses metric units and pounds sterling throughout, so you will need to supply customary units and dollar practice yourself.

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

• Illustrative Mathematics K-5 Math, Grade 4 Free CC BY

  Free through Kendall Hunt. The fraction equivalence and comparison units are the strongest part, and the multiplication progression is built up rather than announced as a rule to follow.

  License: CC BY 4.0. Openly licensed for adaptation with attribution.

• Simply Good and Beautiful Math 4 (The Good and the Beautiful) Free Openly licensed

  120 full-color lessons, free as a PDF, with supporting video lessons posted on the level's FAQ page. More independent than the K-3 levels, which helps if you are teaching several children at once. General Christian worldview throughout.

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

• EngageNY Mathematics, Grade 4 modules Free CC BY-NC-SA

  The fraction modules are among the more carefully built free material at this level, and the long division sequence is patient and thorough. Free PDFs 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 not covered by this license.

• Khan Academy, 4th grade math Free CC BY-NC-SA Not confirmed

  Strong this year for long division practice with step-by-step hints, and for decimal place value. The instant feedback matters when a child is making one small procedural slip over and over.

  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.

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 4 Paid About $100 per year online, verified at $99.99, or roughly $120 to $130 for a printed level.

  Good at: Strong on the conceptual side of fractions and on multi-step problem solving. Children who find standard fourth grade math tedious often come alive here.

  Drawback: Long division and computational fluency get less attention than the standards require, so you will supplement. The difficulty ramps sharply at this level and a struggling child can fall off it entirely.

  Suits: A child who is already fluent and needs harder thinking, not more practice.

• Dimensions Math 4 (Singapore Math Inc.) Paid $14.50 per book, about $58 for student books, more with guides.

  Good at: Bar models make multi-step and fraction word problems tractable in a way few programs manage. The mental math strategies for multiplication are well designed.

  Drawback: Requires the Home Instructor's Guide, and the pace assumes solid mastery of everything from grade 3. A child with shaky facts will drown, and the program will not stop to fix that.

  Suits: A child arriving from a strong third grade, with a parent already comfortable with bar models.

• Math-U-See Delta and Epsilon Paid Roughly $130 to $145 per Level Up Set with blocks owned, and the Fraction Overlay kit is an additional purchase for Epsilon.

  Good at: Delta teaches division to mastery and Epsilon covers fractions with a manipulative system that makes fraction equivalence visible. The fraction overlays are the standout piece of the program.

  Drawback: The topic-per-level structure means fourth grade content is split across two levels, so pacing against grade-level standards takes planning. Geometry, data, and measurement remain thin.

  Suits: A child who needs division or fractions rebuilt from the ground up, taught by a parent willing to map the pacing.

• Saxon Math 5/4 Paid Roughly $130 to $200 for the complete home study kit, varying widely by retailer. Bundles with the Saxon Teacher digital lessons run higher, near $148 at some retailers.

  Good at: Constant cumulative review keeps long division and fact fluency from decaying, which is a common fourth grade failure point. Lessons are short and incremental.

  Drawback: Very light on conceptual explanation, particularly for fractions, and the daily problem sets are long enough to grind a child down. Presentation is dated and plain.

  Suits: A child who forgets procedures without daily revisiting and who tolerates a long problem set.

• Math Mammoth Grade 4 (Light Blue Series) Paid About $40 as a download, approximate, cheaper in a bundle.

  Good at: Thorough coverage of the full standards breadth, clear written explanations aimed at the child, and very inexpensive as a download.

  Drawback: Worksheet-dense and visually plain, and page counts at this level are substantial. Independent-minded children do fine; a child who needs a person talking him through it will not get that here.

  Suits: An independent worker whose parent is teaching several children at once.

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 fourth grade