6.7

6.7 is a knowledge and skills statement. These are the student expectations under it.

• 6.7.A

  generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization

• 6.7.B

  distinguish between expressions and equations verbally, numerically, and algebraically

• 6.7.C

  determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations

• 6.7.D

  generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties

01

What Students Need to Do

Students evaluate numerical expressions in the correct order, including exponents, and break composite numbers into prime factors. They decide whether a mathematical statement is an expression or an equation. They use models and operation properties to rewrite expressions without changing their value.

02

What Mastery Looks Like

A student can evaluate 3² + 24 ÷ 6 accurately and write 60 as 2² × 3 × 5. The student can classify 5x + 2 and 5x + 2 = 17, then show with tiles or algebra that 3(x + 4) and 3x + 12 have the same value. The student can name the property used when rewriting an expression.

03

Common Misconceptions

Students often work strictly left to right, multiply a base by its exponent, or stop before every factor is prime. They may treat the equals sign as a signal that the answer comes next. They may reorder subtraction or division, or distribute to only one term inside parentheses.

04

How to Assess It

Exit ticket: Evaluate 2³ + 18 ÷ 3, write 18 as a prime factorization, and rewrite 4(x + 3) using a property. Label 4(x + 3) and 4x + 12 = 28 as expression or equation, then decide whether 4(x + 3) and 4x + 12 are equivalent.

1. 01

   Give students algebra tiles to build 3(x + 2), then rearrange the tiles to show 3x + 6 and explain why the values match.

2. 02

   Post 4 + 3 and 4 + 3 = 7, then ask students to explain which is an expression and which is an equation.

3. 03

   Play Property Match: students pair cards such as 7 + 0, 4 + 9, and 6(2 + x) with equivalent forms and property names.

4. 04

   Use two phone plans, such as 20 + 5m and 5m + 20, to discuss why different forms can represent the same cost.

• 6.10

  The student applies mathematical process standards to use equations and inequalities to solve problems

• 5.4

  The 5th Grade version of this standard.

• 6.9

  The student applies mathematical process standards to use equations and inequalities to represent situations

• 4.5

  The 4th Grade version of this standard.