Learning Progression

Numbers and Operations: Operational Fluency

Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Algebra I - Module 1 - Operations and Linear Functions & Inequalities	Algebra II - Module 1 - Numbers Systems and Data Analysis
CC.2.1.1.B.3 Use place value concepts and properties of operations to add and subtract within 100. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
CC.2.1.2.B.3 Use place value understanding and properties of operations to add and subtract within 1000. When grade appropriate instruction pertaining to an eligible content should begin	CC.2.1.2.B.3 Use place value understanding and properties of operations to add and subtract within 1000. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
		M03.A-T.1.1.2 Add two- and three-digit whole numbers (limit sums from 100 through 1,000) and/or subtract two- and three-digit numbers from three-digit whole numbers. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
		M03.A-T.1.1.3 Multiply one-digit whole numbers by two-digit multiples of 10 (from 10 through 90). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
			M04.A-T.2.1.1 Add and subtract multi-digit whole numbers (limit sums and subtrahends up to and including 1,000,000). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
			M04.A-T.2.1.2 Multiply a whole number of up to four digits by a one-digit whole number and multiply 2 two-digit numbers. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
			M04.A-T.2.1.3 Divide up to four-digit dividends by one-digit divisors with answers written as whole-number quotients and remainders. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
		M04.A-T.2.1.4 Estimate the answer to addition, subtraction, and multiplication problems using whole numbers through six digits (for multiplication, no more than 2 digits × 1 digit, excluding powers of 10). When grade appropriate instruction pertaining to an eligible content should begin	M04.A-T.2.1.4 Estimate the answer to addition, subtraction, and multiplication problems using whole numbers through six digits (for multiplication, no more than 2 digits × 1 digit, excluding powers of 10). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
			M04.A-F.2.1.1 Add and subtract fractions with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; answers do not need to be simplified; and no improper fractions as the final answer). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
			M04.A-F.2.1.3 Add and subtract mixed numbers with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; no regrouping with subtraction; fractions do not need to be simplified; and no improper fractions as the final answers). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
			M04.A-F.2.1.4 Solve word problems involving addition and subtraction of fractions referring to the same whole or set and having like denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
			M04.A-F.3.1.1 Add two fractions with respective denominators 10 and 100. Example: Express 3/10 as 30/100, and add 3/10 + 4/100 = 30/100 + 4/100 = 34/100. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
			M04.A-F.2.1.5 Multiply a whole number by a unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 5 × (1/4) = 5/4 When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
			M04.A-F.2.1.6 Multiply a whole number by a non-unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 3 × (5/6) = 15/6 When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
			M04.A-F.2.1.7 Solve word problems involving multiplication of a whole number by a fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
				M05.A-T.2.1.1 Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
				M05.A-T.2.1.2 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
				M05.A-F.1.1.1 Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Example: 2/3 + 5/4 = 8/12 + 15/12 = 23/12 When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
				M05.A-T.2.1.3 Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
				M05.A-F.2.1.1 Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
				M05.A-F.2.1.2 Multiply a fraction (including mixed numbers) by a fraction. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
		M05.A-F.2.1.3 Demonstrate an understanding of multiplication as scaling (resizing). Example 1: Comparing 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. Example 2: Explaining 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. When grade appropriate instruction pertaining to an eligible content should begin	M05.A-F.2.1.3 Demonstrate an understanding of multiplication as scaling (resizing). Example 1: Comparing 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. Example 2: Explaining 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. When grade appropriate instruction pertaining to an eligible content should begin	M05.A-F.2.1.3 Demonstrate an understanding of multiplication as scaling (resizing). Example 1: Comparing 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. Example 2: Explaining 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. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
				M05.A-F.2.1.4 Divide unit fractions by whole numbers and whole numbers by unit fractions. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
			M06.A-N.1.1.1 Interpret and compute quotients of fractions (including mixed numbers), and solve word problems involving division of fractions by fractions. Example 1: Given a story context for (2/3) ÷ (3/4), explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc.) Example 2: How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Example 3: How many 2 1/4-foot pieces can be cut from a 15 1/2-foot board? When grade appropriate instruction pertaining to an eligible content should begin	M06.A-N.1.1.1 Interpret and compute quotients of fractions (including mixed numbers), and solve word problems involving division of fractions by fractions. Example 1: Given a story context for (2/3) ÷ (3/4), explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc.) Example 2: How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Example 3: How many 2 1/4-foot pieces can be cut from a 15 1/2-foot board? When grade appropriate instruction pertaining to an eligible content should begin	M06.A-N.1.1.1 Interpret and compute quotients of fractions (including mixed numbers), and solve word problems involving division of fractions by fractions. Example 1: Given a story context for (2/3) ÷ (3/4), explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc.) Example 2: How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Example 3: How many 2 1/4-foot pieces can be cut from a 15 1/2-foot board? When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
					M06.A-N.2.1.1 Solve problems involving operations (+, –, ×, and ÷) with whole numbers, decimals (through thousandths), straight computation, or word problems. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
					M06.A-N.2.2.2 Apply the distributive property to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. Example: Express 36 + 8 as 4(9 + 2). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
					M07.A-N.1.1.1 Apply properties of operations to add and subtract rational numbers, including real-world contexts. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
					M07.A-N.1.1.3 Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
					M06.A-R.1.1.2 Find the unit rate a/b associated with a ratio a:b (with b ≠ 0) and use rate language in the context of a ratio relationship. Example 1: “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” Example 2: “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
				M06.A-R.1.1.4 Solve unit rate problems including those involving unit pricing and constant speed. Example: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? When grade appropriate instruction pertaining to an eligible content should begin	M06.A-R.1.1.4 Solve unit rate problems including those involving unit pricing and constant speed. Example: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
					M06.A-R.1.1.5 Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percentage. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
					M07.A-R.1.1.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. Example: If a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 / 1/4 miles per hour, equivalently 2 miles per hour. When grade appropriate instruction pertaining to an eligible content should begin	M07.A-R.1.1.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. Example: If a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 / 1/4 miles per hour, equivalently 2 miles per hour. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
						M07.A-R.1.1.6 Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease. When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
							A1.1.1.1.2 Simplify square roots (e.g., √24 = 2√6). When grade appropriate instruction pertaining to an eligible content should begin	A1.1.1.1.2 Simplify square roots (e.g., √24 = 2√6). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
							A2.1.1.1.1 Simplify square roots in terms of i. (e.g., √–24 = 2i√6). When grade appropriate instruction pertaining to an eligible content should begin		A2.1.1.1.1 Simplify square roots in terms of i. (e.g., √–24 = 2i√6). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
									A2.1.1.1.2 Simplify/evaluate expressions involving imaginary numbers powers of i (e.g., i⁶ + i³ = –1 + i). When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Learning Progression

Numbers and Operations: Operational Fluency

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