Review place value understanding for numbers within 1,000.

Build numbers to 10,000 and write numbers to that place value in standard, unit, and expanded form. 

Model and write numbers to 10,000 with more than 9 of any unit in standard and unit form.

Build numbers to 1,000,000 and write numbers to that place value in standard and unit form.

Multiply and divide single units by 10. Recognize that a digit represents 10 times the value of what it represents in the place to its right.

Multiply and divide multiple units by 10. Apply the property of “ten times greater” in the context of problems.

Read and write multi-digit numbers using base-ten numerals, number names, and expanded form.

Locate multi-digit numbers on a number line and explain their placement.

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

Round multi-digit numbers to their largest place.

Round multi-digit numbers to any place.

Round multi-digit numbers to any place in more complex cases, including those involving real-world contexts and/or assessing the reasonableness of that estimate. 

Fluently add multi-digit whole numbers using the standard algorithm involving up to two compositions. Solve one-step word problems involving addition.

Fluently add multi-digit whole numbers using the standard algorithm involving multiple compositions. Solve one-step word problems involving addition.

Solve multi-step word problems involving addition, using rounding to assess the reasonableness of answers.

Fluently subtract multi-digit whole numbers using the standard algorithm involving up to two decompositions. Solve one-step word problems involving subtraction.

Fluently subtract multi-digit whole numbers using the standard algorithm involving multiple decompositions. Solve one-step word problems involving subtraction.

Solve multi-step word problems involving subtraction, using rounding to assess the reasonableness of answers.

Solve multi-step word problems involving addition and subtraction, using rounding to assess the reasonableness of answers.

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. Interpret a multiplication equation as a comparison. 

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

Multiply multiples of 10, 100, and 1,000 by one-digit numbers. Estimate multi-digit products by rounding numbers to their largest place value.

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

Multiply two-digit numbers by one-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.