Expressions and Equations – Apply and extend previous understandings of arithmetic to algebraic expressions.
TEACHERS:Terri Pemberton / SUBJECT:6th Grade MathSTANDARD:
- 6.EE.2.c – Evaluate expressions at specific values for their variables.
OBJECTIVE (EXPLICIT):
- Solve expressions for a given value of a variable including those used in formulas.
EVIDENCE OF MASTERY (MEASURABLE):
SUB-OBJECTIVES, SWBAT (SEQUENCED FROM BASIC TO COMPLEX):
- Evaluate an algebraic expression for a given value.
- Substitute values in formulas (perimeter and area)to solve real-world problems.
KEY VOCABULARY:
Substitute
Evaluate
Order of operations / MATERIALS:
20 - Color tiles (represent variable terms)
30 - Color chips (units)
White boards & markers
ENGAGE (MAKE CONTENT AND LEARNING RELEVANT TO REAL LIFE AND CONNECT TO STUDENT INTEREST)It takes4 minutes for the cook to create a burger at Bob’s Burger Barn once it is ordered. If 5 people have placed their order before Tommy, how long will it take Tommy to get his burger?
BEFORE / TEACHER WILL:
- Ask students to create an expression that would find the cost of sundaes for x number of people if the sundaes cost $3.
- Ask students to share their expressions and write them on the board.
- Ask students to “substitute”different values for the variable to determine the total cost of sundaes depending on the number of people ordering them.
- Ask students to brainstorm other uses for expressions where simply substituting a value can change the answer (guide them towards finding perimeter and area).
- Create an expression for the cost of x number of sundaes at $3 each with shoulder partner.
- Share their expression with the class.
- Using a white board, substitutethe given values for the variable to determine the cost depending on the number of people ordering sundaes.
- Brainstorm other uses for expressions where simply substituting a value can change the answer.
DURING / TEACHER WILL:
- Distribute bags of color tiles and chips and remind students that the tiles represent terms with a variable and the chips represent units.
- Model how “3 times a number x” would look using tiles and chips. (Place 3 tiles under document camera)
- Tell students that we are going to substitute 4 for x so that we can evaluate the expression. (Replace each of the 3 tiles with 4 chips each.)
- Count the tiles.
- Guide additional examples for evaluating each expression using order of operations(see attached for sample):
- 15 + x for x = 6.
- 2f – 3 for f = 5.
- 24 ÷ b for b = 3 (guide students to separate 24 into groups of 3)
- 7x for x = 3
- Review the perimeter andarea formulas for rectangles and squares and ask students what the variables represent. (P = s+s+s+s or 4s; A = lw or )
- Draw a square. Tell them that one side is 5 feet long and ask them to use the formulas to find perimeter and area. Ask students to come up with a real world example for how finding the perimeter and area of a shape could be useful.
- Hand out worksheets with additional practice (attached)
- Bring students back together and guide them to discover that as the number being substituted into an expression or a formula changes so does the answer, but the expression or formula does not.
- Separate tiles and chips.
- Follow along with teacher to create a visual representation of “3x” using chips and tiles.
- Use tiles and chips to create a model.
- Count the chips to find the solution.
- Use chips and tiles to solve additional examples then write the expression and its solution on a sheet of paper.
- With shoulder partner, identify what the variables represent in the perimeter and area.
- With shoulder partner, find the perimeter and area of the square drawn on the board. Be able to explain how substitution was used in each expression to evaluate each formula. Discuss a real world example for how finding the perimeter and area of a shape could be useful.
- Use pictures and numbers to complete additional practice worksheet.
- Discuss the importance of the expression or formula in regards to the value being substituted for the variable.
AFTER / TEACHER WILL:
- Ask students the engage question from above. With shoulder partner discuss an answer. How would your time differ if there were 3 people ahead of you? 6? 7?
- Ask students to write a real-word problem using a coefficient, operation and variable. Then, pick a value for the variable to prove their algebraic expression works.
- Additional practice problems: pgs. 14-17
- With your shoulder partner, discuss the answer to the engage question.
- Discuss how the time will differ depending on the number of people ahead of you.
- Create an expression for a real world situation. Write a journal entry explaining how you use substitution to evaluate your expression for a variety of values of your variable.
Examples for student work that can be put in notebook or on a blank piece of paper:
Expression: 15 + x for x = 6 / Expression:2f – 3 for f = 5Picture: OOOOOOOOOOOOOOO
+ OOOOOO = 21 / Picture:
-OOO
OOOOO OOOOO – OOO = 7
Solution: 15 + 6 = 21 / Solution: 2(5) – 3 = 7
Name ______Block_____ Date______
(Practice Worksheet 6.EE.2.c)
Directions: Solve each expression for the given variable. Use pictures and numbers for each problem.
- 8x – 4; when x = 4
Picture: / Numbers:
- (7 + c) ÷4; when c = 5
Picture: / Numbers:
- 8b – (b + 4); when b = 4
Picture: / Numbers:
- + 3y - (z + 4); when x = 2, y = 4, and z = 6.
Pictures: / Numbers:
Answer the following questions keeping in mind the perimeter and area formulas.
- The length of a rectangle is 5 feet and the width is 3 feet. Draw and label the rectangle, then find the perimeter and area. Make sure you label your answers.
Picture: / Perimeter: / Area:
- The area of square is 3 square inches. Draw and label a picture of the square. Then, find the perimeter of the square.
Picture: / Perimeter:
- Find the area and perimeter for the given rectangle.
5 in.5 in.
Perimeter: / Area:8 in.
- Explain how you were able to find the perimeter and area for #7.