Students have practiced solving three different types of percentage problems (corresponding to finding AA, BB, or CC respectively when A% of BB is CC). This lesson focuses on finding “A% of BB” as efficiently as possible. While the previous lesson used numbers that students could calculate mentally, the numbers in this lesson are purposefully chosen to be difficult for students to calculate mentally or to represent on a double number line diagram, so as to motivate them to find the simplest way to do the calculation by hand.
The third activity hints at work students will do in grade 7, namely finding a constant of proportionality and writing an equation to represent a proportional relationship.
 See teacher's lesson notes for solutions
 See video solutions by Mr. Quinn
*Solutions
 Problems

*Solutions
 Problems 1, 2, 3, 4 & 5, 6, 7
*Solutions
 Problems 1, 2, 3, 4 and 5, 6

*Solutions
 Problems (12) , (34) , (56)
Notice: I still expect that you complete the homework on "paper" and then submit your answers using Jupiter Grades (Juno). I you are having issues correcting and submitting your answers online you may bring in the homework on paper and submit it to me instead. Please keep in mind that homework submitted on paper will need to be turned in the day it is due to receive full credit.
*Please use the online aspect as a grading tool. If you miss problems you may "redo" the exercise to receive full credit. Just make sure you are writing the correct answers on your assignment so that when you redo it you can get them correct and receive full credit.
*NOTE: I am not unreasonable and absolutely do not want any tears or frustration in math, so if you are having issues with anything concerning math please just stop and talk with me (at a convenient time). :)
Notice: I still expect that you complete the homework on "paper" and then submit your answers using Jupiter Grades (Juno). I you are having issues correcting and submitting your answers online you may bring in the homework on paper and submit it to me instead. Please keep in mind that homework submitted on paper will need to be turned in the day it is due to receive full credit.
*Please use the online aspect as a grading tool. If you miss problems you may "redo" the exercise to receive full credit. Just make sure you are writing the correct answers on your assignment so that when you redo it you can get them correct and receive full credit.
*NOTE: I am not unreasonable and absolutely do not want any tears or frustration in math, so if you are having issues with anything concerning math please just stop and talk with me (at a convenient time). :)
Notice: I still expect that you complete the homework on "paper" and then submit your answers using Jupiter Grades (Juno). I you are having issues correcting and submitting your answers online you may bring in the homework on paper and submit it to me instead. Please keep in mind that homework submitted on paper will need to be turned in the day it is due to receive full credit.
*Please use the online aspect as a grading tool. If you miss problems you may "redo" the exercise to receive full credit. Just make sure you are writing the correct answers on your assignment so that when you redo it you can get them correct and receive full credit.
*NOTE: I am not unreasonable and absolutely do not want any tears or frustration in math, so if you are having issues with anything concerning math please just stop and talk with me (at a convenient time). :)
*Please complete today's homework in your notebook and be prepared for the class discussion.
Notice: I still expect that you complete the homework on "paper" and then submit your answers using Jupiter Grades (Juno). I you are having issues correcting and submitting your answers online you may bring in the homework on paper and submit it to me instead. Please keep in mind that homework submitted on paper will need to be turned in the day it is due to receive full credit.
*Please use the online aspect as a grading tool. If you miss problems you may "redo" the exercise to receive full credit. Just make sure you are writing the correct answers on your assignment so that when you redo it you can get them correct and receive full credit.
*NOTE: I am not unreasonable and absolutely do not want any tears or frustration in math, so if you are having issues with anything concerning math please just stop and talk with me (at a convenient time). :)
Notice: I still expect that you complete the homework on "paper" and then submit your answers using Jupiter Grades (Juno). I you are having issues correcting and submitting your answers online you may bring in the homework on paper and submit it to me instead. Please keep in mind that homework submitted on paper will need to be turned in the day it is due to receive full credit.
*Please use the online aspect as a grading tool. If you miss problems you may "redo" the exercise to receive full credit. Just make sure you are writing the correct answers on your assignment so that when you redo it you can get them correct and receive full credit.
*NOTE: I am not unreasonable and absolutely do not want any tears or frustration in math, so if you are having issues with anything concerning math please just stop and talk with me (at a convenient time). :)
Notice: I still expect that you complete the homework on "paper" and then submit your answers using Jupiter Grades (Juno). I you are having issues correcting and submitting your answers online you may bring in the homework on paper and submit it to me instead. Please keep in mind that homework submitted on paper will need to be turned in the day it is due to receive full credit.
*Please use the online aspect as a grading tool. If you miss problems you may "redo" the exercise to receive full credit. Just make sure you are writing the correct answers on your assignment so that when you redo it you can get them correct and receive full credit.
*NOTE: I am not unreasonable and absolutely do not want any tears or frustration in math, so if you are having issues with anything concerning math please just stop and talk with me (at a convenient time). :)

Notice: I still expect that you complete the homework on "paper" and then submit your answers using Jupiter Grades (Juno). I you are having issues correcting and submitting your answers online you may bring in the homework on paper and submit it to me instead. Please keep in mind that homework submitted on paper will need to be turned in the day it is due to receive full credit.
*Please use the online aspect as a grading tool. If you miss problems you may "redo" the exercise to receive full credit. Just make sure you are writing the correct answers on your assignment so that when you redo it you can get them correct and receive full credit.
*NOTE: I am not unreasonable and absolutely do not want any tears or frustration in math, so if you are having issues with anything concerning math please just stop and talk with me (at a convenient time). :)
Notice: I still expect that you complete the homework on "paper" and then submit your answers using Jupiter Grades (Juno). I you are having issues correcting and submitting your answers online you may bring in the homework on paper and submit it to me instead. Please keep in mind that homework submitted on paper will need to be turned in the day it is due to receive full credit.
*Please use the online aspect as a grading tool. If you miss problems you may "redo" the exercise to receive full credit. Just make sure you are writing the correct answers on your assignment so that when you redo it you can get them correct and receive full credit.
*NOTE: I am not unreasonable and absolutely do not want any tears or frustration in math, so if you are having issues with anything concerning math please just stop and talk with me (at a convenient time). :)
Notice: I still expect that you complete the homework on "paper" and then submit your answers using Jupiter Grades (Juno). I you are having issues correcting and submitting your answers online you may bring in the homework on paper and submit it to me instead. Please keep in mind that homework submitted on paper will need to be turned in the day it is due to receive full credit.
*Please use the online aspect as a grading tool. If you miss problems you may "redo" the exercise to receive full credit. Just make sure you are writing the correct answers on your assignment so that when you redo it you can get them correct and receive full credit.
*NOTE: I am not unreasonable and absolutely do not want any tears or frustration in math, so if you are having issues with anything concerning math please just stop and talk with me (at a convenient time). :)
Notice: As of February 26th, 2018
Starting on February 26th, 2018 you will also be submitting your homework online. You will be using Juno (JupiterGrades_"Tests & Lessons") to enter and check your answers.
All assignments will be expected to be posted online to receive credit. Please see me if this is an issue about arranging an alternate solution.
Notice: February 26th, 2018
Starting on February 26th, 2018 you will also be submitting your homework online. You will be using Juno (JupiterGrades_"Tests & Lessons") to enter and check your answers.
All assignments will be expected to be posted online to receive credit. Please see me if this is an issue about arranging an alternate solution.
Notice: February 26th, 2018
Starting on February 26th, 2018 you will also be submitting your homework online. You will be using Juno (JupiterGrades_"Tests & Lessons") to enter and check your answers.
All assignments will be expected to be posted online to receive credit. Please see me if this is an issue about arranging an alternate solution.
Students begin the unit by working with linear equations that have single occurrences of one variable, e.g., x + 1 = 5 and 4x = 2
They represent relationships with tape diagrams and with linear equations, explaining correspondences between these representations. They examine values that make a given linear equation true or false, and what it means for a number to be a solution to an equation. Solving equations of the form px=q where px=q pand pqq are rational numbers can produce complex fractions (i.e., quotients of fractions), so students extend their understanding of fractions to include those with numerators and denominators that are not whole numbers.
The second section introduces balanced and unbalanced “hanger diagrams” as a way to reason about solving the linear equations of the first section. Students write linear equations to represent situations, including situations with percentages, solve the equations, and interpret the solutions in the original contexts (MP2), specifying units of measurement when appropriate (MP6). They represent linear expressions with tape diagrams and use the diagrams to identify values of variables for which two linear expressions are equal. Students write linear expressions such as 6(w  4) and 6w  24 and represent them with area diagrams, noting the connection with the distributive property (MP7). They use the distributive property to write equivalent expressions.
In the third section of the unit, students write expressions with wholenumber exponents and wholenumber, fraction, or variable bases. They evaluate such expressions, using properties of exponents strategically (MP5). They understand that a solution to an equation in one variable is a number that makes the equation true when the number is substituted for all instances of the variable. They represent algebraic expressions and equations in order to solve problems. They determine whether pairs of numerical exponential expressions are equivalent and explain their reasoning (MP3). By examining a list of values, they find solutions for simple exponential equations of the form a=b2 and 2x=32 and simple quadratic and cubic equations, e.g., 64=x364=x3.
In the last section of the unit, students represent collections of equivalent ratios as equations. They use and make connections between tables, graphs, and linear equations that represent the same relationships (MP1).
Students begin the unit by working with linear equations that have single occurrences of one variable, e.g., x + 1 = 5 and 4x = 2
They represent relationships with tape diagrams and with linear equations, explaining correspondences between these representations. They examine values that make a given linear equation true or false, and what it means for a number to be a solution to an equation. Solving equations of the form px=q where px=q pand pqq are rational numbers can produce complex fractions (i.e., quotients of fractions), so students extend their understanding of fractions to include those with numerators and denominators that are not whole numbers.
The second section introduces balanced and unbalanced “hanger diagrams” as a way to reason about solving the linear equations of the first section. Students write linear equations to represent situations, including situations with percentages, solve the equations, and interpret the solutions in the original contexts (MP2), specifying units of measurement when appropriate (MP6). They represent linear expressions with tape diagrams and use the diagrams to identify values of variables for which two linear expressions are equal. Students write linear expressions such as 6(w  4) and 6w  24 and represent them with area diagrams, noting the connection with the distributive property (MP7). They use the distributive property to write equivalent expressions.
In the third section of the unit, students write expressions with wholenumber exponents and wholenumber, fraction, or variable bases. They evaluate such expressions, using properties of exponents strategically (MP5). They understand that a solution to an equation in one variable is a number that makes the equation true when the number is substituted for all instances of the variable. They represent algebraic expressions and equations in order to solve problems. They determine whether pairs of numerical exponential expressions are equivalent and explain their reasoning (MP3). By examining a list of values, they find solutions for simple exponential equations of the form a=b2 and 2x=32 and simple quadratic and cubic equations, e.g., 64=x364=x3.
In the last section of the unit, students represent collections of equivalent ratios as equations. They use and make connections between tables, graphs, and linear equations that represent the same relationships (MP1).
Students begin the unit by working with linear equations that have single occurrences of one variable, e.g., x + 1 = 5 and 4x = 2
They represent relationships with tape diagrams and with linear equations, explaining correspondences between these representations. They examine values that make a given linear equation true or false, and what it means for a number to be a solution to an equation. Solving equations of the form px=q where px=q pand pqq are rational numbers can produce complex fractions (i.e., quotients of fractions), so students extend their understanding of fractions to include those with numerators and denominators that are not whole numbers.
The second section introduces balanced and unbalanced “hanger diagrams” as a way to reason about solving the linear equations of the first section. Students write linear equations to represent situations, including situations with percentages, solve the equations, and interpret the solutions in the original contexts (MP2), specifying units of measurement when appropriate (MP6). They represent linear expressions with tape diagrams and use the diagrams to identify values of variables for which two linear expressions are equal. Students write linear expressions such as 6(w  4) and 6w  24 and represent them with area diagrams, noting the connection with the distributive property (MP7). They use the distributive property to write equivalent expressions.
In the third section of the unit, students write expressions with wholenumber exponents and wholenumber, fraction, or variable bases. They evaluate such expressions, using properties of exponents strategically (MP5). They understand that a solution to an equation in one variable is a number that makes the equation true when the number is substituted for all instances of the variable. They represent algebraic expressions and equations in order to solve problems. They determine whether pairs of numerical exponential expressions are equivalent and explain their reasoning (MP3). By examining a list of values, they find solutions for simple exponential equations of the form a=b2 and 2x=32 and simple quadratic and cubic equations, e.g., 64=x364=x3.
In the last section of the unit, students represent collections of equivalent ratios as equations. They use and make connections between tables, graphs, and linear equations that represent the same relationships (MP1).
Students begin the unit by working with linear equations that have single occurrences of one variable, e.g., x + 1 = 5 and 4x = 2
They represent relationships with tape diagrams and with linear equations, explaining correspondences between these representations. They examine values that make a given linear equation true or false, and what it means for a number to be a solution to an equation. Solving equations of the form px=q where px=q pand pqq are rational numbers can produce complex fractions (i.e., quotients of fractions), so students extend their understanding of fractions to include those with numerators and denominators that are not whole numbers.
The second section introduces balanced and unbalanced “hanger diagrams” as a way to reason about solving the linear equations of the first section. Students write linear equations to represent situations, including situations with percentages, solve the equations, and interpret the solutions in the original contexts (MP2), specifying units of measurement when appropriate (MP6). They represent linear expressions with tape diagrams and use the diagrams to identify values of variables for which two linear expressions are equal. Students write linear expressions such as 6(w  4) and 6w  24 and represent them with area diagrams, noting the connection with the distributive property (MP7). They use the distributive property to write equivalent expressions.
In the third section of the unit, students write expressions with wholenumber exponents and wholenumber, fraction, or variable bases. They evaluate such expressions, using properties of exponents strategically (MP5). They understand that a solution to an equation in one variable is a number that makes the equation true when the number is substituted for all instances of the variable. They represent algebraic expressions and equations in order to solve problems. They determine whether pairs of numerical exponential expressions are equivalent and explain their reasoning (MP3). By examining a list of values, they find solutions for simple exponential equations of the form a=b2 and 2x=32 and simple quadratic and cubic equations, e.g., 64=x364=x3.
In the last section of the unit, students represent collections of equivalent ratios as equations. They use and make connections between tables, graphs, and linear equations that represent the same relationships (MP1).
Students begin the unit by working with linear equations that have single occurrences of one variable, e.g., x + 1 = 5 and 4x = 2
They represent relationships with tape diagrams and with linear equations, explaining correspondences between these representations. They examine values that make a given linear equation true or false, and what it means for a number to be a solution to an equation. Solving equations of the form px=q where px=q pand pqq are rational numbers can produce complex fractions (i.e., quotients of fractions), so students extend their understanding of fractions to include those with numerators and denominators that are not whole numbers.
The second section introduces balanced and unbalanced “hanger diagrams” as a way to reason about solving the linear equations of the first section. Students write linear equations to represent situations, including situations with percentages, solve the equations, and interpret the solutions in the original contexts (MP2), specifying units of measurement when appropriate (MP6). They represent linear expressions with tape diagrams and use the diagrams to identify values of variables for which two linear expressions are equal. Students write linear expressions such as 6(w  4) and 6w  24 and represent them with area diagrams, noting the connection with the distributive property (MP7). They use the distributive property to write equivalent expressions.
In the third section of the unit, students write expressions with wholenumber exponents and wholenumber, fraction, or variable bases. They evaluate such expressions, using properties of exponents strategically (MP5). They understand that a solution to an equation in one variable is a number that makes the equation true when the number is substituted for all instances of the variable. They represent algebraic expressions and equations in order to solve problems. They determine whether pairs of numerical exponential expressions are equivalent and explain their reasoning (MP3). By examining a list of values, they find solutions for simple exponential equations of the form a=b2 and 2x=32 and simple quadratic and cubic equations, e.g., 64=x364=x3.
In the last section of the unit, students represent collections of equivalent ratios as equations. They use and make connections between tables, graphs, and linear equations that represent the same relationships (MP1).