Foundations of Algebra

Unit 1: Number Sense

• 8.NS.A.1 Explore the real number system. a. Know the differences between rational and irrational numbers. b. Understand that all rational numbers have a decimal expansion that terminates or repeats. c. Convert decimals which repeat into fractions and fractions into repeating decimals. d. Generate equivalent representations of rational numbers
• 8.NS.A.2 Estimate the value and compare the size of irrational numbers and approximate their locations on a number line.
• 6.NS.C.7 Understand that the absolute value of a rational number is its distance from 0 on the number line.
• 4.RA.B.4 Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number.

Unit 2: Integers

• 7.NS.A.1 Apply and extend previous understandings of numbers to add and subtract rational numbers. a. Add and subtract rational numbers. b. Represent addition and subtraction on a horizontal or vertical number line. c. Describe situations and show that a number and its opposite have a sum of 0 (additive inverses). d. Understand subtraction of rational numbers as adding the additive inverse. e. Determine the distance between two rational numbers on the number line is the absolute value of their difference. f. Interpret sums and differences of rational numbers.
• 7.NS.A.2 Apply and extend previous understandings of numbers to multiply and divide rational numbers. a. Multiply and divide rational numbers. b. Determine that a number and its reciprocal have a product of 1 (multiplicative inverse). c. Understand that every quotient of integers (with non-zero divisor) is a rational number. d. Convert a rational number to a decimal. e. Understand that all rational numbers can be written as fractions or decimal numbers that terminate or repeat. f. Interpret products and quotients of rational numbers by describing real-world contexts.
• 8.EEI.A.1 Explore the real number system. a. Know the differences between rational and irrational numbers. b. Understand that all rational numbers have a decimal expansion that terminates or repeats. c. Convert decimals which repeat into fractions and fractions into repeating decimals. d. Generate equivalent representations of rational numbers
• 8.EEI.A.2 Estimate the value and compare the size of irrational numbers and approximate their locations on a number line.
• 5.RA.B.3 Write, evaluate and interpret numeric expressions using the order of operations.
• 7.EEI.B.4 Solve problems using numerical and algebraic expressions and equations.
• 8.EEI.A.3 Express very large and very small quantities in scientific notation and approximate how many times larger one is than the other.

Unit 3: Fractions

• 5.NF.B.5 Justify the reasonableness of a product when multiplying with fractions. a. Estimate the size of the product based on the size of the two factors. b. Explain why multiplying a given number by a fraction greater than 1 results in a product larger than the given number. c. Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. d. Explain why multiplying the numerator and denominator by the same number is equivalent to multiplying the fraction by 1.
• 5.NF.A.1 Understand the relationship between fractions and decimals (denominators that are factors of 100).
• 5.NF.B.7 Extend the concept of multiplication to multiply a fraction or whole number by a fraction:
  • Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths.
  • Calculate and interpret the product of a fraction by a whole number and a whole number by a fraction.
  • Calculate and interpret the product of two fractions less than one.
• 5.NF.B.8 Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations. a. Calculate and interpret the quotient of a unit fraction by a non-zero whole number. b. Calculate and interpret the quotient of a whole number by a unit fraction.
• 6.NS.A.1 Compute and interpret quotients of positive fractions. a. Solve problems involving division of fractions by fractions.
• 5.NF.B.6 Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution.

Unit 4: Expressions

• 6.EEI.A.2 Create and evaluate expressions involving variables and whole number exponents.
  • a. Identify parts of an expression using mathematical terminology.
  • b. Evaluate expressions at specific values of the variables.
  • c. Evaluate non-negative rational number expressions.
  • d. Write and evaluate algebraic expressions.
  • e. Understand the meaning of the variable in the context of the situation.
• 7.EEI.A.1 Apply properties of operations to simplify and to factor linear algebraic expressions with rational coefficients.
• 6.EEI.A.3 Reason about and solve one-variable equations and inequalities.
• A.SSE.A.1 Interpret the contextual meaning of individual terms or factorsfrom a given problem that utilizes formulas or expressions.