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Grade 4 Math

28 curriculum outcomes with explicit teaching progressions

Select a record to inspect its progression

Operations Algebraic Thinking · 4.OA.A.1

Interpret multiplication as multiplicative comparison

Independently interpret a multiplication equation as a comparison, such as interpreting 35 = 5 × 7 as 35 is 5 times as many as 7 and 7 times as many as 5; represent verbal statements of multiplicative comparisons as multiplication equations. across representations and contexts.

Component progression

  1. 1I can interpret a given multiplication equation, such as 35 = 5 × 7, as a statement of multiplicative comparison.
  2. 2I can write a multiplication equation to represent a verbal statement of multiplicative comparison.
  3. 3I can distinguish a multiplicative comparison ('times as many') from an additive comparison ('more than') in a given statement.
Operations Algebraic Thinking · 4.OA.A.2

Solve multiplicative comparison problems

Independently multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison, using drawings and equations with a symbol for the unknown number. across representations and contexts.

Component progression

  1. 1I can represent a multiplicative comparison word problem using a drawing or diagram.
  2. 2I can solve a multiplicative comparison word problem where the total is unknown, using multiplication.
  3. 3I can solve a multiplicative comparison word problem where a factor is unknown, using division.
Operations Algebraic Thinking · 4.OA.A.3

Solve multistep problems and interpret remainders

Independently solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted, representing the problem using an equation with a symbol for the unknown, and assessing the reasonableness of answers using mental computation and estimation strategies including rounding. across representations and contexts.

Component progression

  1. 1I can write an equation with a symbol for the unknown to represent a multistep whole-number word problem.
  2. 2I can interpret a division problem's remainder appropriately for the context, such as rounding up, dropping it, or reporting it separately.
  3. 3I can use estimation or mental computation to check whether a multistep problem's answer is reasonable.
Operations Algebraic Thinking · 4.OA.B.4

Find factor pairs and classify numbers as prime or composite

Independently find all factor pairs for a whole number in the range 1-100, recognize a number as a multiple of each of its factors, determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number, and determine whether a number in that range is prime or composite. across representations and contexts.

Component progression

  1. 1I can find all factor pairs for a whole number up to 100.
  2. 2I can determine whether a given number up to 100 is a multiple of a given one-digit number.
  3. 3I can classify a whole number up to 100 as prime or composite based on its factor pairs.
Operations Algebraic Thinking · 4.OA.C.5

Generate and analyze number and shape patterns

Independently generate a number or shape pattern that follows a given rule, and identify features of the pattern that were not explicit in the rule itself. across representations and contexts.

Component progression

  1. 1I can generate the terms of a number or shape pattern by correctly applying a given rule.
  2. 2I can identify a feature of a generated pattern, such as alternating even and odd numbers, that wasn't explicitly stated in the rule.
  3. 3I can explain why a discovered pattern feature results from the rule used to generate the pattern.
Number Operations Base Ten · 4.NBT.A.1

Understand place value as ten times the value to the right

Independently recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. across representations and contexts.

Component progression

  1. 1I can compare the value of a digit in one place to the value of the same digit shifted one place to the right, showing it's ten times greater.
  2. 2I can explain, using a place-value model, why each place in a multi-digit number is worth ten times the place to its right.
  3. 3I can use the ten-times relationship to determine the value of a digit given the value of an adjacent digit.
Number Operations Base Ten · 4.NBT.A.2

Read, write, and compare multi-digit numbers

Independently read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form; compare two multi-digit numbers 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 multi-digit whole number using numerals and number names.
  2. 2I can write a multi-digit whole number in expanded form, correctly handling any zero digits.
  3. 3I can compare two multi-digit whole numbers place by place, starting from the highest place value, and record the result with >, =, or <.
Number Operations Base Ten · 4.NBT.A.3

Round multi-digit whole numbers

Independently use place-value understanding to round multi-digit whole numbers to any place. across representations and contexts.

Component progression

  1. 1I can identify the digit in the place being rounded to and the digit immediately to its right.
  2. 2I can round a multi-digit whole number to any specified place using the digit to the right to decide whether to round up or down.
  3. 3I can use rounding to estimate a sum, difference, product, or quotient before computing exactly.
Number Operations Base Ten · 4.NBT.B.4

Fluently add and subtract multi-digit whole numbers

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

Component progression

  1. 1I can correctly align the digits of multi-digit numbers by place value before adding or subtracting.
  2. 2I can add multi-digit whole numbers using the standard algorithm, regrouping as needed.
  3. 3I can subtract multi-digit whole numbers using the standard algorithm, regrouping (borrowing) as needed, including across zeros.
Number Operations Base Ten · 4.NBT.B.5

Multiply multi-digit numbers using place-value strategies

Independently multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations, illustrating and explaining the calculation using equations, rectangular arrays, or area models. across representations and contexts.

Component progression

  1. 1I can multiply a multi-digit number by a one-digit number using an area model that breaks the multi-digit number apart by place value.
  2. 2I can find all necessary partial products when multiplying a multi-digit number by a one- or two-digit number, and combine them for the total.
  3. 3I can multiply two two-digit numbers using a place-value strategy, area model, or rectangular array.
Number Operations Base Ten · 4.NBT.B.6

Divide multi-digit dividends by one-digit divisors

Independently find whole-number quotients and remainders with up to four-digit dividends and one-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 divide a multi-digit dividend by a one-digit divisor by decomposing the dividend by place value.
  2. 2I can use known multiplication facts to find a quotient and check a division using the relationship between multiplication and division.
  3. 3I can find the remainder in a division problem with a multi-digit dividend and interpret it correctly.
Number Operations Fractions · 4.NF.A.1

Explain and generate equivalent fractions

Independently explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) using visual fraction models, attending to how the number and size of the parts differ even though the two fractions themselves are the same size, and use this principle to recognize and generate equivalent fractions. across representations and contexts.

Component progression

  1. 1I can use a visual fraction model, such as fraction bars, to show that two fractions are equivalent.
  2. 2I can explain why multiplying a fraction's numerator and denominator by the same number produces an equivalent fraction.
  3. 3I can generate a fraction equivalent to a given fraction by multiplying the numerator and denominator by the same number.
Number Operations Fractions · 4.NF.A.2

Compare fractions with different numerators and denominators

Independently compare two fractions with different numerators and different denominators by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2, recognizing that comparisons are valid only when the two fractions refer to the same whole, recording the comparison with >, =, or < and justifying the conclusion. across representations and contexts.

Component progression

  1. 1I can compare two fractions by rewriting them with a common denominator.
  2. 2I can compare two fractions by comparing each to a benchmark fraction such as 1/2.
  3. 3I can justify a fraction comparison using a visual model or reasoning about the fractions' sizes, confirming both fractions refer to the same whole.
Number Operations Fractions · 4.NF.B.3

Understand and operate with fractions having like denominators

Independently understand a fraction a/b with a > 1 as a sum of fractions 1/b; understand addition and subtraction of fractions as joining and separating parts referring to the same whole; decompose a fraction into a sum of fractions with the same denominator in more than one way; add and subtract fractions with like denominators, including mixed numbers, and solve word problems involving these operations. across representations and contexts.

Component progression

  1. 1I can decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition as an equation.
  2. 2I can add and subtract fractions with the same denominator, understood as joining or separating parts referring to the same whole, and solve word problems involving these operations.
  3. 3I can add and subtract mixed numbers with like denominators, regrouping between whole numbers and fractions as needed.
Number Operations Fractions · 4.NF.B.4

Multiply a fraction by a whole number

Independently apply and extend previous understanding of multiplication to multiply a fraction by a whole number, understanding a fraction a/b as a multiple of the unit fraction 1/b, and solve word problems involving multiplication of a fraction by a whole number. across representations and contexts.

Component progression

  1. 1I can understand a fraction a/b as a multiple of the unit fraction 1/b, such as recognizing 5/4 as 5 × (1/4).
  2. 2I can multiply a fraction by a whole number by multiplying the numerator by the whole number.
  3. 3I can solve a word problem that requires multiplying a fraction by a whole number.
Number Operations Fractions · 4.NF.C.5

Express tenths as equivalent hundredths

Independently express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. across representations and contexts.

Component progression

  1. 1I can convert a fraction with denominator 10 into an equivalent fraction with denominator 100.
  2. 2I can add a fraction with denominator 10 to a fraction with denominator 100 by first converting the tenths fraction.
  3. 3I can solve a word problem requiring the addition of a fraction with denominator 10 and a fraction with denominator 100.
Number Operations Fractions · 4.NF.C.6

Use decimal notation for fractions

Independently use decimal notation for fractions with denominators 10 or 100, and locate these decimals on a number line. across representations and contexts.

Component progression

  1. 1I can write a fraction with denominator 10 or 100 as its equivalent decimal.
  2. 2I can write a decimal to hundredths as its equivalent fraction with denominator 10 or 100.
  3. 3I can locate a decimal to hundredths at its correct position on a number line.
Number Operations Fractions · 4.NF.C.7

Compare decimals to hundredths

Independently compare two decimals to hundredths by reasoning about their size, recognizing that comparisons are valid only when the two decimals refer to the same whole, and record the comparison with >, =, or <. across representations and contexts.

Component progression

  1. 1I can compare two decimals to hundredths by comparing their tenths and hundredths digits in order.
  2. 2I can explain why two decimals must refer to the same whole for a comparison between them to be valid.
  3. 3I can record the result of comparing two decimals using the >, =, or < symbol.
Measurement Data · 4.MD.A.1

Convert measurements within a system

Independently know relative sizes of measurement units within one system of units, and convert a larger unit's measurement into a smaller unit's measurement, recording conversions in a two-column table. across representations and contexts.

Component progression

  1. 1I can state the relative sizes of measurement units within a single system, such as feet and inches, or kilograms and grams.
  2. 2I can convert a measurement given in a larger unit into an equivalent measurement in a smaller unit.
  3. 3I can record a series of unit conversions in a two-column table showing the relationship between the units.
Measurement Data · 4.MD.A.2

Solve measurement problems using the four operations

Independently use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements in a larger unit as a smaller unit. across representations and contexts.

Component progression

  1. 1I can convert measurements within a word problem to a common unit before solving.
  2. 2I can use an appropriate operation to solve a measurement word problem involving distance, time, volume, mass, or money.
  3. 3I can solve a measurement word problem that involves a simple fraction or decimal quantity.
Measurement Data · 4.MD.A.3

Apply area and perimeter formulas

Independently apply the area and perimeter formulas for rectangles in real-world and mathematical problems. across representations and contexts.

Component progression

  1. 1I can apply the formula length times width to find the area of a rectangle.
  2. 2I can apply a perimeter formula to find the perimeter of a rectangle.
  3. 3I can use the area or perimeter formula to solve for a rectangle's unknown side length given the other measurements.
Measurement Data · 4.MD.B.4

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 (1/2, 1/4, 1/8), and solve problems involving addition and subtraction of fractions using information from the line plot. across representations and contexts.

Component progression

  1. 1I can construct a line plot with a horizontal scale marked in fractional units such as halves, fourths, or eighths.
  2. 2I can plot a data set of measurements given in fractional units on the line plot.
  3. 3I can solve an addition or subtraction problem involving fractions using data displayed on a line plot.
Measurement Data · 4.MD.C.5

Understand angles as fractions of a circle

Independently recognize angles as geometric shapes formed by two rays sharing a common endpoint, and understand concepts of angle measurement, including that an angle is measured as a fraction of the 360-degree circle formed by the ray's rotation. across representations and contexts.

Component progression

  1. 1I can identify an angle as the figure formed by two rays sharing a common endpoint.
  2. 2I can explain that an angle's measure describes the amount of rotation between its two rays, not the length of the rays.
  3. 3I can explain a given angle measure as a fraction of the 360 degrees in a full circle.
Measurement Data · 4.MD.C.6

Measure and draw angles with a protractor

Independently measure angles in whole-number degrees using a protractor, and sketch angles of a specified measure. across representations and contexts.

Component progression

  1. 1I can align a protractor's center point and baseline correctly with an angle's vertex and one ray.
  2. 2I can measure an angle in whole-number degrees using a protractor, reading the correct scale.
  3. 3I can use a protractor to draw an angle with a specified degree measure.
Measurement Data · 4.MD.C.7

Use angle addition to find unknown measures

Independently recognize that an angle measure is additive; when an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts, and solve addition and subtraction problems to find unknown angle measures in a diagram. across representations and contexts.

Component progression

  1. 1I can decompose a given angle into two or more non-overlapping smaller angles.
  2. 2I can write an equation showing that a whole angle's measure equals the sum of its decomposed parts.
  3. 3I can use angle addition to solve for an unknown angle measure in a diagram, given the other angle measures.
Geometry · 4.G.A.1

Draw and identify points, lines, rays, and angles

Independently draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines, and identify these in two-dimensional figures. across representations and contexts.

Component progression

  1. 1I can draw a point, line, line segment, and ray, correctly showing the defining features of each.
  2. 2I can draw right, acute, and obtuse angles, and draw pairs of parallel and perpendicular lines.
  3. 3I can identify points, lines, line segments, rays, angles, and perpendicular or parallel lines within a given two-dimensional figure.
Geometry · 4.G.A.2

Classify shapes by lines and angles

Independently classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size; recognize right triangles as a category and identify right triangles. across representations and contexts.

Component progression

  1. 1I can identify parallel and perpendicular lines within a two-dimensional figure.
  2. 2I can classify a two-dimensional figure based on whether it has parallel lines, perpendicular lines, or angles of a specified size.
  3. 3I can recognize a triangle as a right triangle based on the presence of a right angle, regardless of orientation.
Geometry · 4.G.A.3

Recognize and draw lines of symmetry

Independently recognize a line of symmetry for a two-dimensional figure as a line across which the figure can be folded into matching parts; identify line-symmetric figures and draw lines of symmetry. across representations and contexts.

Component progression

  1. 1I can determine whether a given line through a figure is a line of symmetry by checking whether folding along it produces matching halves.
  2. 2I can identify which of a set of two-dimensional figures have at least one line of symmetry.
  3. 3I can draw all lines of symmetry for a given two-dimensional figure.
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