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Washington Standards

Washington 5th Grade Math Standards

All 30 Washington math standards for 5th grade, each explained in plain English. The official wording is one click away under each one.

30 standards

Data Analysis

6 standards
Formulate statistical investigative questions.
M.5.DA.DS.1
Pose and refine data questions students care about, including ones comparing two variables in one group, like whether classmates who sleep more also run faster.
Official wording
Generate questions of interest to the students that elicit data, generate ideas based on the questions, and refine the question as necessary. Pose statistical questions that can compare two variables withing a group, setting, or situation.
Collect and consider data.
M.5.DA.DS.2
Plan how to collect data, including with technology, and decide how to handle errors like missing values so they do not throw off the results.
Official wording
Determine strategies for collecting and considering data in a variety of ways including with the use of technology. Understand that data may contain errors (missing values, etc.) and decisions have to be made on how to account for or resolve these issues.
Analyze the data.
M.5.DA.DS.3
Use tables, graphs, line plots or spreadsheets as evidence for a claim, and compare different displays to judge which one shows the results most clearly.
Official wording
Critically analyze data visualizations, including tables, bar graphs, line plots, or spreadsheets to support a claim related to the investigative question. Compare and contrast different data visualizations to determine which transparently communicate results and interpretations.
Interpret results.
M.5.DA.DS.4
With teacher guidance, state what the data says about the question and describe how two groups under different conditions differ, like plants grown in sun versus shade.
Official wording
Interpret and communicate results, describing difference between groups, with teacher guidance. Make a statement(s) about the data collected to support the answer to the investigative question. Describe the difference between two groups with different conditions.
Represent data.
M.5.DA.MD.2
Make a line plot of measurements in fractions of a unit and use fraction operations to answer questions, like how much each cup holds if the water is shared evenly.
Official wording
Make a line plot to display a data set of measurements in fractions of a unit. Use operations on fractions to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
Analyze patterns and relationships.
M.5.DA.OA.3
Build two number patterns from two rules, compare their matching terms, and graph the pairs as points on a coordinate grid.
Official wording
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
Common Core 5.OA.3

Quantity

9 standards
Use equivalent fractions as a strategy to add and subtract fractions.
M.5.Q.NF.1
Add and subtract fractions and mixed numbers with different denominators by finding common ones, and justify with models, like 1/3 + 1/4 = 4/12 + 3/12.
Official wording
Add and subtract fractions with unlike denominators (including mixed numbers) using flexible and efficient strategies, including replacing given fractions with equivalent fractions with like denominators. Justify using visual models (e.g., tape diagrams or number lines).
M.5.Q.NF.2
Solve story problems that add or subtract fractions with unlike denominators, and use benchmarks like 1/2 to catch wrong answers, like 1/2 + 1/3 cannot equal 2/5.
Official wording
Efficiently, flexibly, and accurately solve real world word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
M.5.Q.NF.3
See a fraction as a division, like 5 pizzas split among 3 people gives 5/3 each, and solve story problems where dividing whole numbers gives fraction answers.
Official wording
Interpret a fraction as division, where a quantity (the numerator) is divided into equal parts (the denominator). Flexibly and efficiently solve real world word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Assess the reasonableness of answers using estimation strategies. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
M.5.Q.NF.4
Multiply a whole number or fraction by a fraction using models and story contexts, like 2/3 x 6 = 4, and find areas of rectangles with fraction side lengths.
Official wording
Apply and extend previous understandings of multiplication to efficiently, flexibly, and accurately multiply a fraction or whole number by a fraction.aInterpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3, and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15.bFind the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
M.5.Q.NF.5
Predict whether a product will be bigger or smaller than one factor without multiplying, like knowing 3/4 x 12 is less than 12 because 3/4 is less than 1.
Official wording
Interpret multiplication as scaling (resizing) by estimating whether a product will be larger or smaller than a given factor based on the size of the other factor, without performing the indicated multiplication.aComparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.bExplaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a)/(n x b) to the effect of multiplying a/b by 1.
M.5.Q.NF.6
Solve real-world problems that multiply fractions and mixed numbers using models or equations, and check that answers make sense, like 1 1/2 batches of a 2/3 cup recipe.
Official wording
Efficiently and flexibly solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using fraction models or equations to represent the problem. Assess the reasonableness of answers using mental and estimation strategies.
M.5.Q.NF.7
Divide a unit fraction by a whole number or a whole number by a unit fraction with models, like 1/2 ÷ 4 = 1/8 or 3 ÷ 1/4 = 12, and use it in story problems.
Official wording
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions using fraction models and equations to represent the problem.aInterpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3)÷ 4 = 1/12 because (1/12) x 4 = 1/3.bInterpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4.cSolve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Understand the place value system.
M.5.Q.NBT.3
Read and write decimals to thousandths, like 347.392, in words and expanded form, and compare two decimals digit by digit.
Official wording
Read, write, and compare decimals to thousandths.aRead and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).bCompare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Common Core 5.NBT.3
Perform operations with multi-digit whole numbers and with decimals to hundredths.
M.5.Q.NBT.5
Multiply multi-digit whole numbers quickly and correctly with a strategy or the standard method, like 326 x 47.
Official wording
Efficiently, flexibly, and accurately multiply multi-digit whole numbers using strategies or algorithms.

Relationships

7 standards
Write and interpret numerical expressions.
M.5.R.OA.1
Evaluate expressions with parentheses and other grouping symbols, like 3 × (4 + 2), working inside the symbols first.
Official wording
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Common Core 5.OA.1
M.5.R.OA.2
Write expressions that record calculations, like 3 x 12 + 5 for three packs of 12 plus 5 extra, and interpret expressions without working them out.
Official wording
Write expressions that record calculations with numbers and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 x (8+7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
Understand the place value system.
M.5.R.NBT.1
Explain that each place is worth ten times the place to its right and one tenth of the place to its left, like 0.3 is ten times 0.03.
Official wording
Understand that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
M.5.R.NBT.2
Explain how the zeros and the decimal point move when a number is multiplied or divided by a power of 10, and write powers of 10 with exponents.
Official wording
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.
Common Core 5.NBT.2
M.5.R.NBT.4
Use place value to estimate decimals to any place with different strategies, like rounding 7.386 to 7.4 or to 7.39.
Official wording
Use place value understanding of decimals to generate estimates to any place using a variety of estimation strategies.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
M.5.R.NBT.6
Divide whole numbers of up to four digits by two-digit numbers using place value strategies such as partial quotients, arrays or area models, like 1,872 ÷ 24.
Official wording
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors using strategies based on place value, properties of operations, and connected to the relationship between multiplication and division including rectangular arrays, partial quotients, and/or area models.
M.5.R.NBT.7
Add, subtract, multiply and divide decimals to hundredths with models and place value, connect each to a written method and explain why it works, like 2.4 x 0.5.
Official wording
Efficiently, flexibly, and accurately add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Spatial Reasoning

8 standards
Graph points on the coordinate plane to solve real-world and mathematical problems.
M.5.SR.G.1
Plot and locate points on a coordinate grid with an ordered pair like (3, 5), going across on the x-axis first and then up on the y-axis.
Official wording
Use a pair of perpendicular number lines, called axes, to define a coordinate system , with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
Common Core 5.G.1
M.5.SR.G.2
Graph real-world data as points in the first quadrant of a coordinate grid and explain what each point’s coordinates mean.
Official wording
Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.
Common Core 5.G.2
Classify two-dimensional figures into categories based on their properties.
M.5.SR.G.3
Explain that features of a shape category belong to every shape inside it, like all parallelograms have parallel opposite sides, so rhombuses do too.
Official wording
Demonstrate understanding that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
M.5.SR.G.4
Sort flat shapes into groups and subgroups by their sides and angles, like placing squares inside rectangles and rectangles inside parallelograms.
Official wording
Classify two-dimensional figures into categories based on properties.
Convert like measurement units within a given measurement system.
M.5.SR.MD.1
Convert between units in one measurement system, like 3.5 m = 350 cm, and use conversions in multistep real-world problems, checking answers with estimates.
Official wording
Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real world problems. Assess the reasonableness of answers using mental and estimation strategies.
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
M.5.SR.MD.3
Explain volume as the space a solid takes up, measured in unit cubes, so a shape packed with 24 cubes and no gaps has a volume of 24 cubic units.
Official wording
Identify volume as an attribute of solid figures and understand concepts of volume measurement.aA cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.bA solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
M.5.SR.MD.4
Measure volume by counting unit cubes, in cubic centimeters, cubic inches, cubic feet or made-up units.
Official wording
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Common Core 5.MD.4
M.5.SR.MD.5
Find the volume of a box-shaped prism with the formulas V = l × w × h and V = b × h, and add up the volumes of two prisms joined together.
Official wording
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.aFind the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.bApply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.cRecognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Common Core 5.MD.5

The official Washington documents

Washington State Learning Standards for Mathematics by the Office of Superintendent of Public Instruction are available under a Creative Commons Attribution License (CC BY 4.0).

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

The plain-English lines are EMStudio's own explanations, shown beside the official wording. They are not part of the standards.