This document provides guidance for a lesson on solving linear equations. It includes: - Mathematical goals of assessing students' ability to form and solve linear equations using factorizing and the distributive law. - Content standards around using variables, solving word problems, and generating equivalent expressions. - Suggested activities of having students write equations to match stories, discuss their reasoning, and show the steps to solving equations. - Encouragement to have students explain their work and thinking at each stage to help identify misconceptions.

1. Solving Linear Equations
Formative assessment Lesson

2. • Mathematical goals
• This lesson unit is intended to help you assess how well students are able to:
• Form and solve linear equations involving factorizing and using the distributive
law.
• In particular, this unit aims to help you identify and assist students who have
difficulties in:
• Using variables to represent quantities in a real-world or mathematical problem.
• Solving word problems leading to equations of the form px + q = r and p(x + q) = r.
http://map.mathshell.org/lessons.php?unit=7220&collection=8

3. • This lesson asks students to select and apply mathematical content from across
the grades, including the content standards:
• 7.EE:
• Use properties of operations to generate equivalent expressions.
• 7.EE:
• Solve real-life and mathematical problems using numerical and algebraic
expressions and equations.

4. • Questions to ponder after pretest?
• What does x represent?
• How else could you write the expression
• 4(x +7)?
• In 4x + 7 = 80, is adding 7 and then multiplying by 4 the
• same as adding 28? How could you check?
• How do you calculate the area of a rectangle?
• What does perimeter mean?
• What does ‘consecutive’ mean?
What are the three consecutive numbers?
Can you make up a situation that would lead
to the equation 4(x + 3) =16?
• Could you solve these equations using a
different method? What would the method
be? GIVE out whiteboards before going to next slide

5. ANSWER THIS
on a
whiteboard….
Spend time discussing the expressions students give.

6. Write an expression for the perimeter of this rectangle on your whiteboard.
Again, spend time discussing the expressions given by students.

7. Ask students to compare the expressions they have written for A and B with the expression that arises
from the description in C.

8. Write the equations that you think represent
the story on your whiteboard
Discuss the responses given and spend some
time discussing why equations A and D
are correct and why the others are incorrect:
If x is the cost of a notebook, what expression
will give the cost of a pencil?
If a pen costs 3 times as much as a pencil, what
expression will give the cost of a pen?
What mistakes have been made with B and C?
OK, so what is the cost of the notebook?
Can we check that this fits our equations?
Explain to students that in the next activity they
will be writing and matching equations to
stories in a similar way.

9. • Give each student Card Set: Stories (not cut up).
• Here are six stories.
• Spend 5 minutes on your own writing an equation for each of the stories.
• In each case, let x represent the number you are trying to find.
• Do not worry if you can’t write an equation for every story as, later on, you will
be working in groups on this.
• After time is up, get into groups of 2 or 3 and do the next slide.

10. • Organize students into groups of two or three.
• For each group provide a cut-up copy of the Card Set: Stories and Card Set:
Equations.
• The six story cards are the same stories as you have just been looking at.
• Working together in your group, your job is to match each story with an
equation.
• Use the work you have done individually to help you.
• Check to see whether any of the equations you have written down match the
equations on the cards.
• It is likely that students who have identified correct equations may have written
them in a different form to the equations on the card. Encourage them to check
whether what they have written is the same. Some students may have an
incorrect equation, but assume it is correct. Encourage students to check their
work carefully.

11. • Prompt students to explain clearly what expressions mean.
• What does x represent in this story?
• What information do you have? What do you need to find out?
• Encourage students to explain their reasoning carefully and check that all group
members are able to justify each choice.
• Explain please.
• If students finish quickly, ask them to write their own, different stories to match
the equation cards.

12. •SHARING WORK
• After the has made their matches record the matches on a sheet of paper.
• One person moves to another group to concur/share and compare their answers with another group.
Make changes agreed upon and return back to the original groups. Make final changes after everyone
reaches an agreement.
• It is likely that some groups may not have managed to match all six stories with an equation. Spend a
• few minutes discussing some of the matches the students have made. Survey the students to see if,
• after sharing their work with another group, they have changed their mind. Ask them to explain and
• justify their reasoning.
• Did anyone match a different equation with this story? Explain your thinking.
• Which equation is the correct match?
• Did any group change their mind about a match? Which story/equation was it? What did you
• think it was originally? What did you change it to? Explain why you did this.
• The aim of this discussion is to explore the reasoning behind some of the matches and help students
• to justify their thinking, not to check that all groups have successfully matched all of the cards.

13. • Give each group of students a large piece of poster paper, a marker, and a glue stick.
• Put the cards E5 and E6 and the story cards you’ve matched with them to one side.
• Divide your large sheet of paper into quarters.
• You are now going to work with equation cards E1 – E4.
• Stick one at the top of each section, along with the matched story.
• If you haven’t managed to match all four of the equation cards with a story yet, just stick down
• the four equation cards.Teacher guide Solving Linear Equations T-9
• Students don’t need to stick the last two sets of cards in place as they are not used in the second
• matching activity. Nevertheless, if the sheets of paper you have provided are very large, they may
• wish to do this.
• For each group provide a cut-up copy of the Card Set: Steps to Solving.
• You are going to explore the steps to solving these four equations.
• In between each step write a description of the process involved. For example, you may write
• something like ‘divide both sides by 2’ or ‘add 6 to both sides’. Repeat this until you finally reach
• a solution.
• If you find there is more than one method for solving an equation, stick the two solutions side-byside.
• Once students have completed this work, they can finish any matching of pairs. Then encourage them
• to add explanations to their posters to show how they arrived at an equation for each of their chosen
• stories.
• As students work, support them as before. Walk around, watch, listen, and check that students are
• writing a description for each step of the solution process.

14. •Whole-class discussion (15 minutes)
• Select two or three students from different groups that have completed a
solution for Equation Cards E1 and/or E3. Ask them to explain why there are two
methods for solving these equations.
• Which of the two methods is the most efficient?
• Which method do you prefer? Why?
• Is there a different method that could be used to solve these equations?
• What do you need to remember when using the distributive property to clear
parentheses?
• How else could we clear parentheses?
• The focus of this discussion is to explore the processes involved in a range of
different approaches, not to promote a particular method.

15. •POST TEST TIME!
•The End!