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Grade 5 Math

26 curriculum outcomes with explicit teaching progressions

Select a record to inspect its progression

Operations Algebraic Thinking · 5.OA.A.1

Evaluate expressions with grouping symbols

Independently use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. across representations and contexts.

Component progression

  1. 1I can identify which grouping symbol in a nested expression must be evaluated first.
  2. 2I can evaluate a numerical expression containing a single set of parentheses, brackets, or braces.
  3. 3I can evaluate a numerical expression containing nested parentheses, brackets, and braces, working from the innermost outward.
Operations Algebraic Thinking · 5.OA.A.2

Write and interpret numerical expressions

Independently write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them, such as recognizing that 3 × (18932 + 921) is three times as large as 18932 + 921, without calculating the indicated sum or product. across representations and contexts.

Component progression

  1. 1I can write a numerical expression that correctly represents a given verbal description of a calculation.
  2. 2I can describe the relationship between two numerical expressions, such as one being a specified number of times as large as the other, without calculating either.
  3. 3I can compare two numerical expressions by analyzing their structure rather than by computing their values.
Operations Algebraic Thinking · 5.OA.B.3

Generate patterns, form ordered pairs, and graph relationships

Independently 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. across representations and contexts.

Component progression

  1. 1I can generate two numerical patterns from two given rules, applied to the same starting number or corresponding starting numbers.
  2. 2I can identify an apparent relationship between corresponding terms of two generated numerical patterns.
  3. 3I can form ordered pairs from corresponding terms of two patterns and graph them correctly on a coordinate plane.
Number Operations Base Ten · 5.NBT.A.1

Explain place-value relationships across the decimal point

Independently recognize 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. across representations and contexts.

Component progression

  1. 1I can explain that a digit's value is ten times greater than the same digit one place to its right.
  2. 2I can explain that a digit's value is one-tenth of the same digit one place to its left.
  3. 3I can apply the ten-times and one-tenth place-value relationships to digits on either side of a decimal point.
Number Operations Base Ten · 5.NBT.A.2

Explain patterns in powers of ten

Independently explain patterns in the number of zeros of a 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. across representations and contexts.

Component progression

  1. 1I can explain the pattern in the number of zeros when a whole number is multiplied by 10, 100, or 1000.
  2. 2I can explain the pattern in how the decimal point shifts when a decimal is multiplied or divided by a power of 10.
  3. 3I can write a power of 10 using whole-number exponent notation and connect it to the number of zeros or decimal shift.
Number Operations Base Ten · 5.NBT.A.3

Read, write, and compare decimals to thousandths

Independently read and write decimals to thousandths using base-ten numerals, number names, and expanded form, and compare two decimals to thousandths based on the values of the digits in each place, using >, =, and < symbols. across representations and contexts.

Component progression

  1. 1I can read and write a decimal to the thousandths place using numerals and number names.
  2. 2I can write a decimal to thousandths in expanded form, showing the value of each digit.
  3. 3I can compare two decimals to the thousandths place by comparing digits in the same place value, and record the result with >, =, or <.
Number Operations Base Ten · 5.NBT.A.4

Round decimals to any place

Independently use place-value understanding to round decimals to any place. across representations and contexts.

Component progression

  1. 1I can identify the digit in the place a decimal is being rounded to and the digit immediately to its right.
  2. 2I can round a decimal to any specified place using the digit to the right to decide whether to round up or down.
  3. 3I can use decimal rounding to estimate a sum, difference, product, or quotient before computing exactly.
Number Operations Base Ten · 5.NBT.B.5

Fluently multiply multi-digit whole numbers

Independently fluently multiply multi-digit whole numbers using the standard algorithm. across representations and contexts.

Component progression

  1. 1I can multiply a multi-digit number by a one-digit number using the standard algorithm.
  2. 2I can multiply two multi-digit numbers using the standard algorithm, correctly placing placeholder zeros for each partial product.
  3. 3I can add all partial products correctly, aligned by place value, to find the final product.
Number Operations Base Ten · 5.NBT.B.6

Divide multi-digit whole numbers with two-digit divisors

Independently find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, or the relationship between multiplication and division, illustrating and explaining the calculation using equations, rectangular arrays, or area models. across representations and contexts.

Component progression

  1. 1I can estimate a quotient digit for a division problem with a two-digit divisor using place-value reasoning.
  2. 2I can divide a multi-digit dividend by a two-digit divisor using an area model or partial-quotients strategy.
  3. 3I can check a division result by multiplying the quotient by the divisor and comparing to the original dividend.
Number Operations Base Ten · 5.NBT.B.7

Add, subtract, multiply, and divide decimals to hundredths

Independently add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, or the relationship between addition and subtraction, relating the strategy to a written method and explaining the reasoning used. across representations and contexts.

Component progression

  1. 1I can add and subtract decimals to hundredths, aligning decimal points correctly.
  2. 2I can multiply decimals to hundredths, correctly placing the decimal point in the product based on the factors' decimal places.
  3. 3I can divide decimals to hundredths using a place-value strategy or model.
Number Operations Fractions · 5.NF.A.1

Add and subtract fractions with unlike denominators

Independently add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in a way that produces an equivalent sum or difference of fractions with like denominators. across representations and contexts.

Component progression

  1. 1I can find a common denominator for two fractions with unlike denominators.
  2. 2I can rewrite two fractions with unlike denominators as equivalent fractions sharing a common denominator.
  3. 3I can add or subtract fractions, including mixed numbers, after rewriting them with a common denominator.
Number Operations Fractions · 5.NF.A.2

Solve fraction word problems and assess reasonableness

Independently solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, and use benchmark fractions and number sense to estimate mentally and assess the reasonableness of answers. across representations and contexts.

Component progression

  1. 1I can represent a word problem involving addition or subtraction of fractions referring to the same whole.
  2. 2I can solve a fraction addition or subtraction word problem, including cases with unlike denominators.
  3. 3I can use benchmark fractions to estimate an answer mentally and assess whether a computed answer is reasonable.
Number Operations Fractions · 5.NF.B.3

Interpret a fraction as division

Independently interpret a fraction as the division of the numerator by the denominator (a/b = a ÷ b), and solve word problems involving division of whole numbers leading to fraction or mixed-number answers. across representations and contexts.

Component progression

  1. 1I can explain that a fraction a/b represents the division a divided by b.
  2. 2I can represent a whole-number division word problem as a fraction when the quotient is not a whole number.
  3. 3I can solve a word problem involving division of whole numbers whose answer is a fraction or mixed number.
Number Operations Fractions · 5.NF.B.4

Multiply fractions using visual models

Independently apply and extend understanding of multiplication to multiply a fraction or whole number by a fraction: interpret the product (a/b) × q as a parts of a partition of q into b equal parts, equivalently as the result of the sequence of operations a × q ÷ b, and find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, showing that the area is the same as would be found by multiplying the side lengths. across representations and contexts.

Component progression

  1. 1I can use a visual model to multiply a fraction by a whole number.
  2. 2I can use an area model to multiply a fraction by a fraction and find the product.
  3. 3I can multiply two fractions by multiplying their numerators and multiplying their denominators, connecting the result to the area model.
Number Operations Fractions · 5.NF.B.5

Interpret multiplication as scaling

Independently interpret multiplication as scaling (resizing) by comparing the size of a product to the size of one factor based on the size of the other factor without performing the multiplication, explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and why multiplying by a fraction less than 1 results in a product smaller than the given number, and relate the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a fraction by 1. across representations and contexts.

Component progression

  1. 1I can predict whether a product will be greater than or less than a given factor, based on the size of the other factor, without calculating.
  2. 2I can explain why multiplying a number by a fraction greater than 1 produces a larger product, and why multiplying by a fraction less than 1 produces a smaller product.
  3. 3I can relate the fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a fraction by 1, connecting it to the scaling interpretation of multiplication.
Number Operations Fractions · 5.NF.B.6

Solve real-world fraction multiplication problems

Independently solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations to represent the problem. across representations and contexts.

Component progression

  1. 1I can convert a mixed number to an improper fraction in preparation for multiplication.
  2. 2I can represent a real-world fraction or mixed-number multiplication problem with a visual model or equation.
  3. 3I can solve a real-world problem involving multiplication of fractions or mixed numbers.
Number Operations Fractions · 5.NF.B.7

Divide unit fractions and whole numbers

Independently apply and extend understanding of division to divide a unit fraction by a whole number and a whole number by a unit fraction, using visual fraction models and equations to represent and solve the problem. across representations and contexts.

Component progression

  1. 1I can use a visual model to divide a unit fraction by a whole number, showing the fraction being partitioned further.
  2. 2I can use a visual model to divide a whole number by a unit fraction, showing how many fractional pieces fit into the whole number.
  3. 3I can solve a word problem involving division of a unit fraction by a whole number, or a whole number by a unit fraction.
Measurement Data · 5.MD.A.1

Convert measurement units within a system

Independently convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multistep, real-world problems. across representations and contexts.

Component progression

  1. 1I can convert a measurement between different-sized units within the same measurement system.
  2. 2I can identify and perform a needed unit conversion as part of solving a multistep real-world measurement problem.
  3. 3I can solve a multistep real-world problem that requires converting and then combining measurements.
Measurement Data · 5.MD.B.2

Make and interpret line plots with fractional measurements

Independently make a line plot to display a data set of measurements in fractions of a unit (halves, quarters, and eighths), and use operations on fractions to solve problems involving information presented in the line plot. across representations and contexts.

Component progression

  1. 1I can construct a line plot with an accurately spaced fractional horizontal scale.
  2. 2I can plot a data set of fractional measurements on the constructed line plot.
  3. 3I can use addition, subtraction, or division of fractions to solve a problem involving data displayed on a line plot.
Measurement Data · 5.MD.C.3

Understand volume as an attribute measured in cubic units

Independently recognize volume as an attribute of solid figures, understand concepts of volume measurement, and understand that a solid figure packed without gaps or overlaps using n unit cubes represents a volume of n cubic units. across representations and contexts.

Component progression

  1. 1I can explain volume as the amount of space a three-dimensional solid figure occupies.
  2. 2I can explain that a cubic unit is a cube with a specific unit edge length, used to measure volume.
  3. 3I can explain that packing a solid with n unit cubes, without gaps or overlaps, means the solid has a volume of n cubic units.
Measurement Data · 5.MD.C.4

Measure volume by counting unit cubes

Independently measure volumes by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units. across representations and contexts.

Component progression

  1. 1I can count the number of unit cubes that make up a given solid figure, including cubes not directly visible.
  2. 2I can measure a solid's volume in cubic centimeters, cubic inches, or cubic feet by counting unit cubes.
  3. 3I can measure a solid's volume using an improvised (non-standard) cubic unit by counting how many fit.
Measurement Data · 5.MD.C.5

Relate volume to multiplication and addition

Independently relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume, including showing that packing a right rectangular prism with unit cubes gives the same volume as multiplying its edge lengths, applying the formulas v = l × w × h and v = b × h for rectangular prisms with whole-number edge lengths, and finding volumes of solid figures composed of two non-overlapping right rectangular prisms by adding their volumes. across representations and contexts.

Component progression

  1. 1I can show that packing a right rectangular prism with unit cubes gives the same volume as multiplying its edge lengths, or equivalently multiplying the base area by the height.
  2. 2I can apply the formulas v = l × w × h and v = b × h, where b is the base area, to find the volume of a right rectangular prism with whole-number edge lengths.
  3. 3I can find the total volume of a solid figure composed of two non-overlapping rectangular prisms by adding their individual volumes, applying the property that volume is additive.
Geometry · 5.G.A.1

Use axes, the origin, and ordered pairs on a coordinate plane

Independently use a pair of perpendicular number lines (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, understanding that the first number indicates the distance to travel from the origin along one axis and the second number indicates the distance to travel along the other axis, with the convention that the axis names and coordinates correspond (x-axis with x-coordinate, y-axis with y-coordinate). across representations and contexts.

Component progression

  1. 1I can identify the x-axis, y-axis, and origin of a coordinate plane.
  2. 2I can plot a point on a coordinate plane given its ordered pair of coordinates, moving correctly along the x-axis then the y-axis.
  3. 3I can identify the ordered pair of coordinates for a point already plotted on a coordinate plane.
Geometry · 5.G.A.2

Graph and interpret points for real-world problems

Independently 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. across representations and contexts.

Component progression

  1. 1I can graph a set of real-world data points in the first quadrant of the coordinate plane.
  2. 2I can interpret the meaning of a point's coordinates in terms of the original real-world situation.
  3. 3I can use graphed points to answer a question about the real-world or mathematical situation they represent.
Geometry · 5.G.B.3

Understand attributes define categories of shapes

Independently understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category, such as all rectangles having four right angles, and squares being rectangles, so all squares have four right angles. across representations and contexts.

Component progression

  1. 1I can identify the defining attributes shared by all members of a category of two-dimensional shapes, such as all rectangles.
  2. 2I can identify the additional attributes that distinguish a subcategory, such as squares, from the broader category of rectangles.
  3. 3I can explain why an attribute of a broader category must also apply to all its subcategories.
Geometry · 5.G.B.4

Classify shapes in a hierarchy

Independently classify two-dimensional figures in a hierarchy based on their properties. across representations and contexts.

Component progression

  1. 1I can identify the relevant properties of a given two-dimensional figure needed for classification.
  2. 2I can place a two-dimensional figure correctly within a hierarchy of shape categories and subcategories based on its properties.
  3. 3I can construct a hierarchy diagram organizing a set of two-dimensional shapes into categories and subcategories based on shared properties.
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