|Unit: Expressions and Equations|
|Grade Level: 6|
|CCSS Covered:||6.EE.A.1, 6.EE.A.2a, 6.EE.A.2b, 6.EE.A.2c, 6.EE.A.2d, 6.EE.A.3, 6.EE.A.4, 6.EE.B.4, 6.EE.B.5, 6.EE.B.6, 6.EE.B.7, 6.EE.B.8, 6.EE.C.8, 6.EE.C.9, 6.NS.B.4,6.NS.C.8,|
1. Write and evaluate numerical expressions involving whole-number exponents.
For example 2^3 = 8 (CC.6.EE.1)
2. Write variable expressions when solving a real-world or mathematical problem
3. Recognize that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
|4. Write expressions that record operations with numbers and with letters standing for numbers. |
For example, express the calculation “Subtract y from 5” as 5 – y.
|5. Identify the parts of an expression using mathematical terms |
-term, coefficient, constant, variable
-sum, difference, product, quotient
|6. Evaluate expressions at specific values of their variables. |
7. Evaluate expressions that arise from formulas used in real-world problems.
8. Demonstrate an understanding of arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
For example, use the formulas V = s^3 and A = 6s^2 to find the volume and surface area of a cube with sides of lengths s = 1/2.
|9. Apply the identity properties to generate equivalent expressions.|
10. Apply the associative properties to generate equivalent expressions.
11. Apply the commutative properties to generate equivalent expressions.
12. Apply the distributive properties to generate equivalent expressions.
For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
|13. Identify and show when two expressions are equivalent |
For example, the expressions y + y + y and 3y are equivalent because the name the same number regardless of which number y stands for.
|14. Determine whether a given number in a specified set makes an equation or inequality true.|
|15. Write variable expressions when solving a real-world or mathematical problem|
16. Recognize that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
|17. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.|
|18. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. 19. Recognize that inequalities of the form x> c or x < c have infinitely many solutions|
20. Represent solutions of inequalities on number line diagrams.
|21. Define independent and dependent variables.|
22. Use variables to represent two quantities in a real-world problem that change in relationship to one another. 23. Write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable.
24. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
1. Solve real-world problems by graphing points in all four quadrants of the coordinate plane.
2. Calculate distances between points with the same first coordinate or the same second coordinate using coordinates.
3. Calculate distances between points with the same first coordinate or the same second coordinate using absolute value.
|4. Describe one or more parts of an expression as a single entity. |
For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both as single entity and a sum of two terms.
|5. Solve problems using multi-digit numbers and find common factors and multiples. |
6. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. 7. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
For example, express 36 + 8 as 4 (9 + 2). (CC.6.NS.4)
|Essential Questions||Evidence of Mathematical Practices|
|1. What is equivalence?|
2. How are properties of operations used to prove equivalence?
3. How are variables defined and used?
4. How does the structure of equations and/or inequalities help us solve equations
5. How does the substitution process help in solving problems?
6. Why are variables used in equations?
7. What might a variable represent in a given situation?
8. How are inequalities represented and solved?
9. How do ordered pairs on coordinate graphs help define relationships?
10.How do we determine if a variable is independent or dependent in an expression