On Core Mathematics Grade 6 TEACHER EDITION AND ASSESSMENT GUIDE SAMPLER Teacher Edition and Assessment Guide Sampler includes: - On Core Program Overview - Table of Contents for Grade 6 - Teaching Support and Student Lessons - Assessments Bridge the gap between your program and the Common Core State Standards. A complete program of activities, practice, and assessment for each Common Core State Mathematics Standard.
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On Core MathematicsGrade 6
Teacher ediTion and
assessmenT Guide sampler
Teacher Edition and Assessment Guide Sampler includes:
- On Core Program Overview
- Table of Contents for Grade 6
- Teaching Support and Student Lessons
- Assessments
Bridge the gap between your program and the Common Core State Standards. A complete program of activities, practice, and assessment for each Common Core State Mathematics Standard.
On Core Mathematics is a comprehensive, ready-made resource providing instruction, practice and assessment for each Common Core State Mathematics Standard at your grade level. Designed to be used hand-in-hand with your current elementary math series, On Core offers you a flexible way to fill in any gaps between your series and the new standards. Whether you use just the lessons you need, or decide use the entire student workbook for comprehensive Common Core coverage, On Core provides a complete Common Core solution in just four components:
student edition: provides a searchable database of additional worksheets, projects, and hands-on activities correlated to the Common Core State Standards. Helps teachers focus on the mathematical practices.
Teacher edition: Instructional support for each Common Core Standards lesson. The three part, research-based lesson plan (Introduce, Teach, and Practice), that uses manipulatives and powerful visual models, provides everything needed to use the content.
assessment Guide: One page of assessment for each standard in multiple-choice, free-response and constructed response formats.
Exam View® online assessment: Administer premade print or online assessments or create your own with this powerful online tool aligned to the Common Core Standards.
13. Michaela is hiking on a weekend camping trip. She has walked 6 miles so far. This is 30% of the total distance. What is the total number of miles she will walk?
14. A customer placed an order with a bakery for cupcakes. The baker has completed 37.5% of the order after baking 81 cupcakes. How many cupcakes did the customer order?
You can use equivalent ratios to find the whole, given a part and the percent.
percent 5 part _____ whole
60% 5 54 __ j
60 4 20 ________ 100 4 20
5 54 __ j
3 _ 5 5 54 __
n
3 3 18 ______ 5 3 18
5 54 __ n
54 __ 90
5 54 __ n
54 is 60% of what number?
Step 1 Write the relationship among the percent, part, and whole. The percent is 60%. The part is 54. The whole is unknown.
Step 2 Write the percent as a ratio.
Step 3 Simplify the known ratio.
• Find the GCF of the numerator and denominator.
60 5 2 3 2 3 3 3 5
100 5 2 3 2 3 5 3 5
• Divide both the numerator and denominator by the GCF.
Step 4 Write an equivalent ratio.
• Look at the numerators. Think: 3 3 18 5 54
• Multiply the denominator by 18 to fi nd the whole.
So, 54 is 60% of 90.
Find the unknown value.
60 ___ 100
5 54 __ j
Lesson Objective: Find the whole given a part and the percent.
GCF 5 2 3 2 3 5 5 20
1. 12 is 40% of n
2. 15 is 25% of n
3. 24 is 20% of n
4. 36 is 50% of n
5. 4 is 80% of n
6. 12 is 15% of n
7. 36 is 90% of n
8. 12 is 75% of n
9. 27 is 30% of n
30 60 120
72 5 80
40 16 90
About the MathThe relationship among the part, percent, and whole can be used to find the whole when the percent and part are given. Students will support their learning when they look for and express regularity in repeated reasoning.
The LessonIntroduce Remind students that they have used equivalent ratios to find the part, given the percent and the whole. In this lesson they will use equivalent ratios to find the whole, given the percent and the part.
Teach Point out to students that both ratios in Step 2 represent part ____ whole . A percent
is part out of 100, so 60 is the part and 100 is the whole. In the second ratio, 54 is the part and the whole is unknown.
Explain to students that simplifying the known ratio makes it easier to find the equivalent ratio.
Extend the process of finding the whole given a part and the percent by having students estimate first. Then have them check to see if their answers are reasonable.
Practice Have students complete page 28. You may wish to review the process by discussing the first exercise.
Find the Whole from a Percent
COMMON CORE STANDARDCC.6.RP.3c
OBJECTIVEFind the whole given a part and the percent.
ESSENTIAL QUESTIONHow can you find the whole given a part and the percent?
13. Michaela is hiking on a weekend camping trip. She has walked 6 miles so far. This is 30% of the total distance. What is the total number of miles she will walk?
14. A customer placed an order with a bakery for cupcakes. The baker has completed 37.5% of the order after baking 81 cupcakes. How many cupcakes did the customer order?
Use one or more exponents to write the expression.
Find the value.
1. 6 3 6
____
2. 11 3 11 3 11 3 11
____
3. 9 3 9 3 9 3 9 3 7 3 7
____
4. 9 2
____
5. 6 4
____
6. 1 6
____
7. 8 3
____
8. 10 5
____
9. 23 2
____
10. Write 144 with an exponent by using 12 as the base.
11. Write 343 with an exponent by using 7 as the base.
12. Each day Sheila doubles the number of push-ups she did the day before. On the fifth day, she does 2 3 2 3 2 3 2 3 2 push-ups. Use an exponent to write the number of push-ups Shelia does on the fifth day.
13. The city of Beijing has a population of more than 10 7 people. Write the population of Beijing without using an exponent.
6 2 11 4 9 4 3 7 2
81
512
12 2
2 5 more than 10,000,000
7 3
100,000
1,296 1
529
LESSON 49Pages 97–98Page 49, Assessment Guide
Exponents
About the MathExponents can be considered as a shorthand method for representing repeated multiplication. Students will be able to relate powers of 10 to the base-ten number system. Each place value is 10 times the place to its right. Students will support their learning when they look for and make use of structure.
The LessonIntroduce Remind students that multiplication is an easier way of writing repeated addition of the same addend. Then tell them that in this lesson they will learn an easier way to represent repeated multiplication of the same factor, such as 2 3 2 3 2 3 2 3 2 3 2 3 2.
Teach Discuss the meaning of exponent and base with the students. The exponent tells how many times a number is used as a factor. The base is the number that is being multiplied repeatedly. So, the multiplication above can be written as 2 7 . Have students write a multiplication expression with a repeated factor for a partner to evaluate.
Extend the process of writing expressions with exponents to include two different repeated factors. Then have students determine the exponent for a product, given the base.
Practice Have students complete page 98. You may wish to review the process by discussing the first exercise.
COMMON CORE STANDARDCC.6.EE.1
OBJECTIVEWrite and evaluate expressions involving exponents.
ESSENTIAL QUESTIONHow do you write and find the value of expressions involving exponents?
Use one or more exponents to write the expression.
Find the value.
1. 6 3 6
____
2. 11 3 11 3 11 3 11
____
3. 9 3 9 3 9 3 9 3 7 3 7
____
4. 9 2
____
5. 6 4
____
6. 1 6
____
7. 8 3
____
8. 10 5
____
9. 23 2
____
10. Write 144 with an exponent by using 12 as the base.
11. Write 343 with an exponent by using 7 as the base.
12. Each day Sheila doubles the number of push-ups she did the day before. On the fifth day, she does 2 3 2 3 2 3 2 3 2 push-ups. Use an exponent to write the number of push-ups Shelia does on the fifth day.
13. The city of Beijing has a population of more than 10 7 people. Write the population of Beijing without using an exponent.
6 2 11 4 9 4 3 7 2
81
512
12 2
2 5 more than 10,000,000
7 3
100,000
1,296 1
529
LESSON 49Pages 97–98Page 49, Assessment Guide
Exponents
About the MathExponents can be considered as a shorthand method for representing repeated multiplication. Students will be able to relate powers of 10 to the base-ten number system. Each place value is 10 times the place to its right. Students will support their learning when they look for and make use of structure.
The LessonIntroduce Remind students that multiplication is an easier way of writing repeated addition of the same addend. Then tell them that in this lesson they will learn an easier way to represent repeated multiplication of the same factor, such as 2 3 2 3 2 3 2 3 2 3 2 3 2.
Teach Discuss the meaning of exponent and base with the students. The exponent tells how many times a number is used as a factor. The base is the number that is being multiplied repeatedly. So, the multiplication above can be written as 2 7 . Have students write a multiplication expression with a repeated factor for a partner to evaluate.
Extend the process of writing expressions with exponents to include two different repeated factors. Then have students determine the exponent for a product, given the base.
Practice Have students complete page 98. You may wish to review the process by discussing the first exercise.
COMMON CORE STANDARDCC.6.EE.1
OBJECTIVEWrite and evaluate expressions involving exponents.
ESSENTIAL QUESTIONHow do you write and find the value of expressions involving exponents?
Use one or more exponents to write the expression.
Find the value.
1. 6 3 6
____
2. 11 3 11 3 11 3 11
____
3. 9 3 9 3 9 3 9 3 7 3 7
____
4. 9 2
____
5. 6 4
____
6. 1 6
____
7. 8 3
____
8. 10 5
____
9. 23 2
____
10. Write 144 with an exponent by using 12 as the base.
11. Write 343 with an exponent by using 7 as the base.
12. Each day Sheila doubles the number of push-ups she did the day before. On the fifth day, she does 2 3 2 3 2 3 2 3 2 push-ups. Use an exponent to write the number of push-ups Shelia does on the fifth day.
13. The city of Beijing has a population of more than 10 7 people. Write the population of Beijing without using an exponent.
Use one or more exponents to write the expression.
Find the value.
1. 6 3 6
____
2. 11 3 11 3 11 3 11
____
3. 9 3 9 3 9 3 9 3 7 3 7
____
4. 9 2
____
5. 6 4
____
6. 1 6
____
7. 8 3
____
8. 10 5
____
9. 23 2
____
10. Write 144 with an exponent by using 12 as the base.
11. Write 343 with an exponent by using 7 as the base.
12. Each day Sheila doubles the number of push-ups she did the day before. On the fifth day, she does 2 3 2 3 2 3 2 3 2 push-ups. Use an exponent to write the number of push-ups Shelia does on the fifth day.
13. The city of Beijing has a population of more than 10 7 people. Write the population of Beijing without using an exponent.
1. A box of pens costs $3 and a box of markers costs $5. The expression 3p 1 5p represents the cost in dollars to make p packages that includes 1 box of pens and 1 box of markers. Simplify the expression by combining like terms.
2. On a heating bill, a gas company charges customers two different fees based on t therms used. The service fee costs $0.25 per therm and the distribution fee costs $0.10 per therm. The expression 0.25t 1 0.10t 1 40 represents the total bill in dollars. Simplify the expression by combining like terms.
3. A radio show lasts for h hours. During that time, there are 60 minutes of air time per hour and 8 minutes of commercials per hour. The expression 60h 2 8h represents the air time in minutes available for talk and music. Simplify the expression by combining like terms.
4. A publisher sends 100 books to each bookstore where its books are sold. About 3 books are sold at a discount to employees and about 40 books are sold during store supersales. The expression 100s 2 3s 2 40s represents the number of books for s stores that are sold at full price. Simplify the expression by combining like terms.
5. A sub shop sells a meal that includes an Italian sub for $6 and chips for $2. If a customer purchases more than 3 meals, he or she receives a $5 discount. The expression 6m 1 2m 2 5 shows the cost in dollars of the customer’s order for m $ 3. Simplify the expression by combining like terms.
Lesson Objective: Combine like terms by applying the strategy use a model.
COMMON CORE STANDARD CC.6.EE.3
Lesson 54
Problem Solving • Combine Like TermsUse a bar model to solve the problem.
Each hour a company assembles 10 bikes and then packages 6 of those bikes for local shipment. An employee tests 1 bike each day. The expression 10h 2 6h 2 1 represents the number of bikes produced for international shipment in h hours. Simplify the expression by combining like terms.
Read the Problem
What do I need to fi nd?
I need to simplify the
expression .
What information do I need to use?
I need to use the like terms
10h and .
How will I use the information?
I can use a bar model to fi nd the difference of
the terms.
Draw a bar model to subtract from . Each square represents h, or 1h.
Solve the Problem
The model shows that 10h 2 6h 5 . 10h 2 6h 2 1 5 2 1
So, a simplifi ed expression for the number of bikes is .
1. Bradley sells produce in boxes at the local farmer’s market. He put 6 ears of corn and 9 tomatoes in each box. The expression 6b 1 9b represents the total pieces of produce in b boxes. Simplify the expression by combining like terms.
2. Andre bought pencils in packs of 8. He gave 2 pencils to his sister and 3 pencils from each pack to his friends. The expression 8p 2 3p 2 2 represents the number of pencils Andre has left from p packs. Simplify the expression by combining like terms.
h h h h h h h
h h h h h h
h h h
10 h
6 h 4 h
10h – 6h – 1
15b
6hlike
6h
4h
10h
4h
4h 2 1
5p 2 2
About the MathVariables can be used to write expressions when solving problems. Expressions containing like terms can be simplified by combining like terms. Students will support their learning when they model with mathematics.
The LessonIntroduce Remind students that they have used variables to write expressions. In this lesson they will simplify expressions.
Teach Discuss the meaning of like terms as terms that have the same variable to the same power. Remind students that constants are like terms. The model shows that 10h in the first row and 6h in the second row can be combined, in this case subtracted. Have students cross out 6h from each row to show that there are 4h left. Point out that 1 is a constant and does not have the variable h so it cannot be combined.
Extend the process of combining like terms to include adding or subtracting the coefficients of the like terms to combine.
Practice Have students complete page 108. You may wish to review the process by discussing the first exercise.
Problem Solving • Combine Like Terms
COMMON CORE STANDARDCC.6.EE.3
OBJECTIVECombine like terms by applying the strategy use a model.
ESSENTIAL QUESTIONHow can you use the strategy use a model to combine like terms?
VOCABULARYlike terms
MATERIALS
PREREQUISITESWrite and evaluate algebraic expressions.
Lesson Objective: Combine like terms by applying the strategy use a model.
COMMON CORE STANDARD CC.6.EE.3
Lesson 54
Problem Solving • Combine Like TermsUse a bar model to solve the problem.
Each hour a company assembles 10 bikes and then packages 6 of those bikes for local shipment. An employee tests 1 bike each day. The expression 10h 2 6h 2 1 represents the number of bikes produced for international shipment in h hours. Simplify the expression by combining like terms.
Read the Problem
What do I need to fi nd?
I need to simplify the
expression .
What information do I need to use?
I need to use the like terms
10h and .
How will I use the information?
I can use a bar model to fi nd the difference of
the terms.
Draw a bar model to subtract from . Each square represents h, or 1h.
Solve the Problem
The model shows that 10h 2 6h 5 . 10h 2 6h 2 1 5 2 1
So, a simplifi ed expression for the number of bikes is .
1. Bradley sells produce in boxes at the local farmer’s market. He put 6 ears of corn and 9 tomatoes in each box. The expression 6b 1 9b represents the total pieces of produce in b boxes. Simplify the expression by combining like terms.
2. Andre bought pencils in packs of 8. He gave 2 pencils to his sister and 3 pencils from each pack to his friends. The expression 8p 2 3p 2 2 represents the number of pencils Andre has left from p packs. Simplify the expression by combining like terms.
1. A box of pens costs $3 and a box of markers costs $5. The expression 3p 1 5p represents the cost in dollars to make p packages that includes 1 box of pens and 1 box of markers. Simplify the expression by combining like terms.
2. On a heating bill, a gas company charges customers two different fees based on t therms used. The service fee costs $0.25 per therm and the distribution fee costs $0.10 per therm. The expression 0.25t 1 0.10t 1 40 represents the total bill in dollars. Simplify the expression by combining like terms.
3. A radio show lasts for h hours. During that time, there are 60 minutes of air time per hour and 8 minutes of commercials per hour. The expression 60h 2 8h represents the air time in minutes available for talk and music. Simplify the expression by combining like terms.
4. A publisher sends 100 books to each bookstore where its books are sold. About 3 books are sold at a discount to employees and about 40 books are sold during store supersales. The expression 100s 2 3s 2 40s represents the number of books for s stores that are sold at full price. Simplify the expression by combining like terms.
5. A sub shop sells a meal that includes an Italian sub for $6 and chips for $2. If a customer purchases more than 3 meals, he or she receives a $5 discount. The expression 6m 1 2m 2 5 shows the cost in dollars of the customer’s order for m $ 3. Simplify the expression by combining like terms.
2. A train is traveling from Orlando, Florida to Atlanta, Georgia. So far, it has traveled 75% of the distance, or 330 miles. How far is Orlando from Atlanta?
A 247 miles
B 255 miles
C 405 miles
D 440 miles
3. Carmen has saved 80% of the money she needs to buy a new video game. If she has saved $36, how much does the video game cost?
A $28.80 C $63.80
B $45 D $80
4. The sixth-graders at Amir’s school voted for the location of their class trip. The table shows the results.
Class Trip Votes
Location Percent
History Museum 25%
Art Museum 35%
Aquarium 40%
If 126 students voted for going to the art museum, how many sixth-graders are at Amir’s school?
A 226 C 360
B 315 D 504
5. Marcus is saving money to buy a new DVD player. So far, he has saved 60% of the money he needs, or $45. What is the cost of the DVD player? Explain how you know.
$75; I needed to answer the question, “60% of what
5. James wrote 256 as 2 8 . Janet wrote 256 as 4 4 . Explain how you know both of the students are correct. Write a word problem for which Janet’s representation could be used to answer the question.
1. The bill with the greatest value ever printed in the United States had a value of 10 5 dollars. Which is another way to write that amount?
A $10,000
B $50,000
C $100,000
D $500,000
2. Carlos represented 729 with a base and an exponent. Which of the following is NOT possible?
A The base is less than the exponent.
B The base and the exponent are equal.
C The base and the exponent are multiples of 3.
D The base is an odd number and the exponent is an even number.
3. John is making a patio in his yard. He needs a total of 15 2 concrete blocks to cover the area. How many blocks does John need?
A 30
B 125
C 152
D 225
4. Which is a way to write 2 3 2 3 2 3 5 3 5 with exponents and two bases?
A 2 3 3 5 2
B 3 2 3 2 5
C 2 5 3 5 5
D 2 5 3 10 3 5
2 8 means 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2. I grouped the 2s
by 2 to get 4 3 4 3 4 3 4. Then I multiplied 16 by 16, which
is 256. Since my second step was equivalent to 4 4 , I know
the two numbers are equivalent. Possible word problem:
Janet baked cookies for the bake sale. She put 4 cookies
in a bag and 4 bags in a basket. Then she put 4 baskets in
a box. Finally, she put 4 boxes in a bin. How many cookies
1. Sandwiches cost $5, French fries cost $3, and drinks cost $2. The expression 5n 1 3n 1 2n gives the total cost in dollars for buying a sandwich, French fries, and a drink for n people. Which is another way to write this expression?
A 10n
B 10 n 3
C 30n
D 30 n 3
2. Jackets cost $15 and decorative buttons cost $5. The delivery fee is $5 per order. The expression 15n 1 5n 1 5 gives the cost in dollars of buying jackets with buttons for n people. Which is another way to write this expression?
A 25n
B 25 n 2
C 20n 1 5
D 20 n 2 1 5
3. Dana has n quarters. Ivan has 2 fewer than three times the number of quarters Dana has. The expression n 1 3n 2 2 gives the number of quarters they have altogether. Which is another way to write this expression?
A 2 n 2
B 2n
C 4 n 2 2 2
D 4n 2 2
4. Scarves cost $12 and snowmen pins cost $2. Shipping is $3 per order. The expression 12n 1 2n 1 3 gives the cost in dollars of buying scarves with pins for n people. Which is another way to write this expression?
A 14 n 2 1 3
B 14n 1 3
C 17 n 2
D 17n
5. Debbie is n years old. Edna is 3 years older than Debbie, and Shawn is twice as old as Edna. The expression n 1 n 1 3 1 2 3 (n 1 3) gives the sum of their ages. Simplify the expression by combining like terms. Explain how you found your answer.
4n 1 9; First, I used the Distributive Property to rewrite
the expression as n 1 n 1 3 1 (2 3 n) 1 (2 3 3), or
1. Sandwiches cost $5, French fries cost $3, and drinks cost $2. The expression 5n 1 3n 1 2n gives the total cost in dollars for buying a sandwich, French fries, and a drink for n people. Which is another way to write this expression?
A 10n
B 10 n 3
C 30n
D 30 n 3
2. Jackets cost $15 and decorative buttons cost $5. The delivery fee is $5 per order. The expression 15n 1 5n 1 5 gives the cost in dollars of buying jackets with buttons for n people. Which is another way to write this expression?
A 25n
B 25 n 2
C 20n 1 5
D 20 n 2 1 5
3. Dana has n quarters. Ivan has 2 fewer than three times the number of quarters Dana has. The expression n 1 3n 2 2 gives the number of quarters they have altogether. Which is another way to write this expression?
A 2 n 2
B 2n
C 4 n 2 2 2
D 4n 2 2
4. Scarves cost $12 and snowmen pins cost $2. Shipping is $3 per order. The expression 12n 1 2n 1 3 gives the cost in dollars of buying scarves with pins for n people. Which is another way to write this expression?
A 14 n 2 1 3
B 14n 1 3
C 17 n 2
D 17n
5. Debbie is n years old. Edna is 3 years older than Debbie, and Shawn is twice as old as Edna. The expression n 1 n 1 3 1 2 3 (n 1 3) gives the sum of their ages. Simplify the expression by combining like terms. Explain how you found your answer.
4n 1 9; First, I used the Distributive Property to rewrite
the expression as n 1 n 1 3 1 (2 3 n) 1 (2 3 3), or