Fifth grade math

Fifth grade closes out elementary arithmetic and points at algebra. Decimals extend to thousandths and get multiplied and divided. Fractions with unlike denominators get added and subtracted, and fraction multiplication and division start. Order of operations arrives with parentheses and brackets, volume of rectangular prisms shows up, and the coordinate plane makes its first appearance. TEKS adds a financial literacy strand on taxes and budgeting that Common Core does not include. Our rooms cover place value, decimals, fractions, operations, order of operations, measurement, and multi-step problems. Coordinate graphing, volume, and financial literacy are gaps.

• K
• 1st
• 2nd
• 3rd
• 4th
• 5th

What to aim for this year

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

• Represents the value of a digit in decimals through the thousandths using expanded notation
• Compares and orders decimals to the thousandths
• Multiplies a three-digit number by a two-digit number using the standard algorithm
• Divides a four-digit dividend by a two-digit divisor
• Finds products of decimals to the hundredths and quotients of decimals to the hundredths
• Adds and subtracts fractions with unequal denominators referring to the same whole
• Multiplies a whole number by a fraction, and divides a unit fraction by a whole number and a whole number by a unit fraction
• Simplifies numerical expressions using order of operations, including parentheses and brackets
• Distinguishes volume from area and finds the volume of a rectangular prism
• Graphs ordered pairs in the first quadrant of the coordinate plane
• Represents data with bar graphs, dot plots, scatterplots, and stem-and-leaf plots
• Defines income tax, payroll tax, sales tax, and property tax, and balances a simple budget (TEKS financial literacy)

Free, and legal to use

Every one of these costs nothing. The license tag says what you may actually do with it, which is not the same question as whether it is free to read.

• MEP Primary, Year 6 (CIMT) Free Free to use

  The final primary year, with demanding multi-step problems and a pre-algebra flavor that suits the transition ahead. It uses metric units and pounds sterling, so supply customary and dollar practice separately.

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

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

  Free through Kendall Hunt. The units on multiplying and dividing fractions explain why the procedures work instead of handing over invert-and-multiply, which is unusual at this level and worth having.

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

• EngageNY Mathematics, Grade 5 modules Free CC BY-NC-SA

  Thorough on decimal place value and on fraction division, with careful models introduced before any procedure. Free PDFs from the New York State archive, and a lot of printing.

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

• Simply Good and Beautiful Math 5 (The Good and the Beautiful) Free Openly licensed

  120 full-color lessons, free as a PDF, with supporting video lessons on the level's FAQ page. The independence suits a fifth grader who can work alone for a stretch. General Christian worldview throughout.

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

• Khan Academy, 5th grade math Free CC BY-NC-SA Not confirmed

  Well suited to this year's procedural load. Decimal operations, fraction division, and order of operations all benefit from immediate feedback. Also useful as a quick diagnostic before starting pre-algebra.

  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.

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

  Good at: Prepares a child for competition-style thinking and for algebra, with substantial material on fractions and multi-step reasoning. The problems demand more than a typical fifth grade program does.

  Drawback: Coverage does not line up neatly with fifth grade standards, so measurement, data, and the TEKS personal financial literacy strand will be missing. It is also a poor fit for a child who is behind, since it assumes strength.

  Suits: A strong fifth grader headed toward an accelerated middle school track.

• Dimensions Math 5 (Singapore Math Inc.) Paid $14.50 per book, about $58 for student books, more with guides.

  Good at: Strong on fraction and decimal operations, with models that keep the meaning attached to the procedure. Prepares well for a Singapore-track middle school sequence.

  Drawback: Requires the Home Instructor's Guide, and it moves fast. A child with gaps from fourth grade will struggle, because the program assumes mastery rather than rebuilding it.

  Suits: A child who has done Dimensions before and is staying on that track.

• Math-U-See Epsilon and Zeta Paid Roughly $130 to $145 per Level Up Set with blocks owned, plus the Fraction Overlay kit for Epsilon.

  Good at: Epsilon handles fractions and Zeta handles decimals and percents, both with manipulatives that make the concepts visible. For a child who has never really understood fractions, Epsilon is often the fix.

  Drawback: The split across two levels means fifth grade content does not map to a single book, and geometry, data, and statistics stay thin throughout. Pacing against standards requires you to plan it.

  Suits: A child arriving at fifth grade with fractions still broken, where repair matters more than pace.

• Saxon Math 6/5 Paid Roughly $130 to $200 for the home study kit, varying widely by retailer and often discounted well below list.

  Good at: Steady incremental lessons with heavy review, which keeps decimal and fraction procedures from slipping. Reasonable preparation for a traditional algebra track.

  Drawback: Explanations are procedural rather than conceptual, so a child can execute fraction division with no idea what it means. Long daily problem sets and a dated, dense presentation.

  Suits: A child heading for a traditional algebra sequence who needs procedures kept sharp.

• Math Mammoth Grade 5 (Light Blue Series) Paid About $40 as a download, approximate, cheaper in a bundle. Grades 5-8 together run about $113 on sale.

  Good at: Complete standards coverage, explanations written directly to the student, and inexpensive. The decimal and fraction chapters are clearly taught.

  Drawback: Plain black-and-white pages and heavy problem counts, which can wear down a child already tired of arithmetic. Printing at this level is substantial.

  Suits: An independent fifth grader on a tight budget who does not mind a workbook.

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.

What a week looks like

1. Five days, about an hour, and let him work alone for part of it.
2. Two days on fractions, two on decimals, one on order of operations or geometry.
3. Keep /times in the warm-up. Fact speed still decays and now it costs him more.
4. Have him check his own work against the answer key and find his own mistakes before you look.
5. Once a week, do something with money: sales tax on a receipt, a budget, a unit price comparison.

Practice it here, free

These rooms on this site cover part of the year's work. No sign-up, and they work offline.

• place — Decimal place value through thousandths
• column — Multi-digit multiplication and long division
• money — Decimal operations in money contexts
• frac — Adding, subtracting, and multiplying fractions
• times — Fact fluency maintenance under a heavier load
• steps — Order of operations and multi-step expressions
• share — Division, including dividing with fractions
• measure — Measurement and unit conversion
• treasure — Multi-step problem solving practice

The rest of fifth grade