4th Grade

Review place value understanding for numbers within 1,000.

Build and write numbers up to 10,000 in different ways.

Represent numbers up to 10,000 with more than 9 of any unit in numeral and unit form.

Build numbers up to 1,000,000 and write numbers up to 1,000,000 in numeral and unit form.

Understand that a digit represents 10 times the value of what it represents in the place to its right.

Apply “ten times as many/much” language when problem solving.

Read and write multi-digit numbers using numeral form, word form, and expanded form. Convert between forms.

Locate, plot, and label multi-digit whole numbers on a number line and explain their placement.

Compare numbers based on the meanings of the digits and use >, <, or = to record the comparison.

Round multi-digit whole numbers to their largest place and use $$\approx$$ to record the result.

Round multi-digit whole numbers to any place.

Round multi-digit whole numbers to any place in context.

Fluently add multi-digit whole numbers using the standard algorithm.

Solve one-step word problems involving addition.

Solve multi-step word problems involving addition.

Fluently subtract multi-digit whole numbers using the standard algorithm.

Solve one-step word problems involving subtraction.

Solve multi-step word problems involving addition and subtraction.

Solve a 3-Act task involving the addition and subtraction of multi-digit whole numbers.

Solve multiplicative comparison problems with a larger unknown. Distinguish multiplicative comparison from additive comparison.

Solve multiplicative comparison problems with a smaller unknown.

Solve multiplicative comparison problems with an unknown multiplier.

Multiply one- and two-digit numbers by 10, 100, and 1,000.

Multiply one-digit numbers by multiples of 10, 100, and 1,000.

Estimate products and solutions to multiplicative comparison with larger unknown problems.

Multiply one-digit numbers by two-digit numbers using an area model. Solve one-step word problems involving multiplication.

Multiply one-digit numbers by two-, three-, and four-digit numbers.

Multiply three-digit numbers by one-digit numbers.

Multiply four-digit numbers by one-digit numbers.

Multiply two-, three-, and four-digit numbers by one-digit numbers and assess the reasonableness of the product.

Multiply two-digit multiples of 10 by two-digit multiples of 10. Estimate multi-digit products by rounding numbers to their largest place value.

Multiply two-digit multiples of 10 by two-digit numbers.

Multiply two-digit numbers by two-digit numbers using a variety of mental strategies.

Multiply two-digit by two-digit numbers using four partial products.

Multiply two-digit by two-digit numbers using two partial products and assess the reasonableness of the product.

Abstract the formulas for the area and perimeter of a rectangle and apply those formulas in real-world and mathematical problems involving multiplication, addition, and subtraction.

Solve two-step word problems involving multiplication, addition, and subtraction.

Solve multi-step word problems involving multiplication, addition, and subtraction.

Solve division word problems with remainders.

Solve division word problems that require the interpretation of the remainder.

Divide multiples of 10, 100, and 1,000 by one-digit numbers.

Divide two-, three-, and four-digit numbers by one-digit numbers using a variety of mental strategies.

Solve two-digit dividend division problems with no remainder or a remainder in the ones place with smaller divisors and quotients.

Solve two-digit dividend division problems with a remainder in the tens and/or ones place with smaller divisors and quotients.

Solve two-digit dividend division problems with a remainder in any place with larger divisors and quotients.

Solve three-digit dividend division problems with a remainder in any place.

Solve four-digit dividend division problems with a remainder in any place.

Solve two-, three-, and four-digit dividend problems, including the special cases of having a 0 in the quotient or dividend, and assess the reasonableness of the quotient.

Apply the formulas for area and perimeter in real-world and mathematical problems involving all four operations.

Solve two-step word problems involving all four operations, including those involving interpreting the remainder.

Solve multi-step word problems involving all four operations.

Identify and extend growing number patterns.

Identify and extend growing shape patterns.

Identify and extend repeating shape patterns.

Identify multiples and determine if a whole number is a multiple of another number.

Explore patterns in multiples of various whole numbers.

Find factor pairs for numbers to 100 and recognize that a whole number is a multiple of each of its factors.

Determine whether a given number is prime or composite.

Recognize and generate equivalent fractions with smaller units using tape diagrams.

Recognize and generate equivalent fractions with smaller units using number lines.

Recognize and generate equivalent fractions with smaller units using area models.

Recognize and generate equivalent fractions with smaller units using multiples.

Recognize and generate equivalent fractions with larger units using visual models.

Recognize and generate equivalent fractions with larger units using factors.

Compare two fractions where one numerator or denominator is a factor of the other by replacing one fraction with an equivalent one.

Compare two fractions by replacing both fractions with equivalent ones.

Compare two fractions using one whole as a benchmark.

Compare two fractions using one half as a benchmark.

Compare and order fractions using various strategies.

Decompose fractions as a sum of unit fractions and as a multiple of a unit fraction.

Decompose fractions as a sum of fractions with the same denominator in more than one way.

Add and subtract fractions within 1 with the same units.

Solve word problems that involve the addition and subtraction of fractions where the total is less than or equal to one.

Decompose non-unit fractions less than 2 as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction.

Add and subtract fractions that require regrouping where the total is less than 2.

Add two fractions where one denominator is a multiple of the other using the denominators 2, 3, 4, 5, 6, 8, 10, and 12.

Decompose and compose non-unit fractions greater than two as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction.

Convert fractions greater than 1 to mixed numbers.

Convert mixed numbers to fractions greater than 1.

Compare and order fractions greater than 1 using various methods.

Add fractions and mixed numbers where the total is greater than or equal to 2.

Subtract fractions and mixed numbers where the total is greater than or equal to 2.

Add and subtract mixed numbers using a variety of mental strategies.

Solve word problems involving addition and subtraction of fractions.

Multiply a whole number by a fraction.

Multiply a whole number by a mixed number.

Solve word problems involving multiplication of fractions.

Solve word problems involving addition, subtraction, and multiplication of fractions.

Make a line plot (dot plot) representation to display a data set of measurements in fractions of a unit.

Solve problems using information presented in line plots.

Represent decimals to tenths less than or equal to one with area models. Write a decimal value in fraction, decimal, and unit form.

Represent decimals to tenths greater than one with pictorial base ten blocks. Write a decimal value in fraction, decimal, unit, and fraction and decimal expanded form.

Represent decimals to hundredths less than one, understanding the equivalence of some number of tenths and ten times as many hundredths. Write a decimal value in fraction, decimal, and unit form.

Represent decimals to hundredths more than one. Write a decimal value in fraction, decimal, unit, and decimal and fraction expanded form for some number to hundredths.

Regroup decimal numbers with more than 9 tenths or 9 hundredths into simplest unit form and vice versa.

Locate decimals on a number line and explain their placement.

Compare two decimals, recording the result of a comparison with the symbol >, =, or <, and justify the conclusion.

Compare two or more decimals written in various forms.

Add tenths with hundredths written as decimal fractions.

Add tenths with hundredths written as decimals.

Solve word problems involving the addition of decimals and decimal fractions.

Find the value of some combination of dollar bills and coins.

Solve word problems involving money.

Express metric length measurements in terms of a smaller unit, recording measurement equivalents in a two-column table. Solve one-step word problems that require metric length unit conversion.

Express metric mass and capacity measurements in terms of a smaller unit, recording measurement equivalents in a two-column table. Solve one-step word problems that require metric mass or capacity unit conversion.

Know and relate metric units to place value units in order to express measurements in different units.

Solve multi-step word problems that requires metric unit conversions of length, mass, and capacity.

Express customary length measurements in terms of a smaller unit, recording measurement equivalents in a two-column table. Solve one-step word problems that require customary length unit conversion.

Express customary weight measurements in terms of a smaller unit, recording measurement equivalents in a two-column table. Solve one-step word problems that require customary weight unit conversion.

Express customary capacity measurements in terms of a smaller unit, recording measurement equivalents in a two-column table. Solve one-step word problems that require customary capacity unit conversion.

Express time measurements in terms of a smaller unit, recording measurement equivalents in a two-column table. Solve one-step word problems that require time unit conversion.

Solve multi-step word problems involving conversion of customary units of length, weight, capacity, and time.

Express fractional measurements in terms of a smaller unit.

Express decimal measurements in terms of a smaller unit.

Solve word problems involving converting fractional and decimal measurements to a smaller unit.

Identify and draw points, lines, line segments, rays, and angles.

Identify and draw right, obtuse, and acute angles.

Identify and draw perpendicular lines.

Identify and draw parallel lines.

Use iteration with one physical nonstandard unit to measure benchmark angles.

Understand that an angle that turns through $${{1\over360}}$$ of a circle is called a “one-degree angle” and can be used to measure angles. Use a makeshift protractor to measure benchmark angles.

Measure angles that are less than 180° using a 180° protractor. Distinguish angle measure from other attributes.

Sketch angles of specified measure using a 180° protractor.

Identify and measure angles as turns and recognize them in various contexts.

Decompose angles using pattern blocks.

Solve problems involving the measure of two adjacent angles.

Solve problems involving the measure of more than two adjacent angles.

Measure and sketch angles that are greater than 180°.

Analyze and classify triangles based on side length, angle measure, or both.

Draw triangles from given criteria.

Analyze and classify quadrilaterals based on parallel and perpendicular lines and the presence or absence of angles of a specified size.

Draw quadrilaterals from given criteria.

Identify and draw lines of symmetry in two-dimensional figures.