Arizona Standards
Arizona 5th Grade Math Standards
All 35 Arizona math standards for 5th grade, each explained in plain English. The official wording is in Arizona Department of Education's document, linked at the end of this page.
35 standards
Operations and Algebraic Thinking
4 standards5.OA.A.1
Work out expressions that contain parentheses and brackets by following the order of operations, starting with the innermost grouping.
5.OA.A.2
Write expressions for calculations described in words and read what an expression means without solving it, like seeing 3 times a sum is triple that sum.
5.OA.B.3
Build two number patterns from two rules, explain how matching terms relate, and graph the pairs, like add 3 and add 6 giving terms twice as big.
5.OA.B.4
Recognize that a prime number has exactly two factors and break whole numbers down into their prime factors, like 12 = 2 × 2 × 3.
Numbers and Operations in Base Ten
7 standards5.NBT.A.1
Use place value, multiplication and division to explain that a digit is worth ten times more one place left and a tenth as much one place right.
5.NBT.A.2
Explain the patterns in zeros when multiplying by 10, 100 or 1,000 and how the decimal point shifts when a decimal is multiplied or divided by them.
5.NBT.A.3
Read and write decimals to thousandths, like 347.392, in words and expanded form, and compare two decimals digit by digit.
5.NBT.B.5
Multiply multi-digit whole numbers quickly and accurately with a standard algorithm, like 324 × 46.
5.NBT.B.6
Find whole-number quotients when the number being divided has up to four digits and the divisor has two, like 1,872 ÷ 24 = 78.
5.NBT.B.7
Compute sums, differences, products and quotients of decimals to hundredths with models, drawings and place value strategies, then match each to written work.
Number and Operations – Fractions
7 standards5.NF.A.1
Add and subtract fractions and mixed numbers with unlike denominators by rewriting them with a common denominator, like 1/2 + 2/3 = 3/6 + 4/6.
5.NF.A.2
Solve word problems that add or subtract fractions of one whole using models and equations, and estimate with benchmarks like 1/2 to check answers.
5.NF.B.3
Read a fraction as its numerator divided by its denominator, like 3/4 = 3 ÷ 4, and solve sharing problems with fraction or mixed number answers.
5.NF.B.4
Multiply a fraction by a whole number or another fraction using models and stories, and find rectangle areas with fraction sides by tiling and multiplying.
5.NF.B.5
Tell, without multiplying, whether a product will be bigger or smaller than one factor, since multiplying by a fraction less than 1 shrinks a number.
5.NF.B.6
Solve real-world problems that multiply fractions and mixed numbers, showing the work with equations, models and other representations.
5.NF.B.7
Divide a unit fraction by a whole number and a whole number by a unit fraction, like 1/3 ÷ 4 = 1/12 and 4 ÷ 1/5 = 20, and use this in real-world problems.
Measurement and Data
5 standards5.MD.A.1
Convert between larger and smaller units in the same measurement system, like feet to inches, and use those conversions in multi-step real-life problems.
5.MD.B.2
Make line plots of measurements in halves, quarters and eighths, and use fraction operations to answer questions about the data, like sharing juice evenly.
5.MD.C.3
Understand volume as the space inside a solid, measured by how many unit cubes fill it without gaps or overlaps.
5.MD.C.4
Measure volume by counting unit cubes, in cubic centimeters, cubic inches, cubic feet or made-up units.
5.MD.C.5
Find volumes of rectangular prisms by packing unit cubes and with V = l × w × h or V = B × h, and add the volumes of two joined prisms in real problems.
Geometry
4 standards5.G.A.1
Describe the coordinate plane as two perpendicular number lines crossing at the origin, and name first-quadrant points by their across and up distances.
5.G.A.2
Graph real-world data as points in the first quadrant of a coordinate grid and explain what each point’s coordinates mean.
5.G.B.3
Explain that every property of a shape category also belongs to its subcategories, like squares having all the features of rectangles.
5.G.B.4
Sort two-dimensional shapes into a hierarchy by their properties, like quadrilaterals, then parallelograms, then rectangles, then squares.
Standards for Mathematical Practice
8 standards5.MP.1
Make sense of a multi-step fraction or volume problem, plan an approach, and keep working through it when the first try does not succeed.
5.MP.2
Move between numbers and their meaning, like turning a recipe story into 3/4 × 2 and then explaining what the answer says about the recipe.
5.MP.3
Explain and defend answers to fifth grade problems, like why a decimal product can be smaller, and judge whether a classmate's reasoning holds up.
5.MP.4
Use equations, line plots and drawings to model everyday situations, like working out how many cubes fill a box using volume.
5.MP.5
Pick the right tool for fifth grade work, like unit cubes for volume, a ruler for line plot data, or graph paper for plotting coordinates.
5.MP.6
Use exact math words and units, like cubic centimeters for volume, and compute with decimals and fractions carefully to the right place value.
5.MP.7
Spot how numbers are built, like seeing that multiplying by 10 shifts every digit one place left, and use that structure to simplify work.
5.MP.8
Notice repeated steps in calculations, like the shortcut for multiplying fractions, and turn them into general methods while checking answers make sense.
The official Arizona documents
- Arizona Mathematics Standards: Fifth Grade · adopted December 2016 · since 2018-19
The plain-English lines on this page are EMStudio's own explanations of Arizona's standards, not the official wording, which Arizona Department of Education publishes in the documents above. Codes and strand names identify each standard.