Lesson 8.28.2 Small Group · Group 2
Start hereWords, worked example, and sentence starters
Learning target I can solve one-step addition and subtraction equations using inverse operations, explain why the method works, and use it on a problem I have not seen before.
Why This Matters This is your challenge small group for Lesson 8.2. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| EquationSpanish: Ecuación | A math sentence with an equal sign showing both sides are the same. | x + 25 = 60 — both sides equal 60 when x = 35 |
| Inverse operationSpanish: Operación inversa | Two math actions that undo each other, like × and ÷. | + and − |
| IsolateSpanish: Despejar | To get the letter by itself on one side. | get x by itself |
| SolutionSpanish: Solución | A number that makes the equation or inequality true. | x = 7 is the solution to x + 5 = 12 because 7 + 5 = 12 ✓ |
| One-step equationSpanish: Ecuación de un paso | An equation you can solve in a single step using one inverse operation. | x + 7 = 20 |
| BalanceSpanish: Equilibrio | Keeping both sides of an equation equal by doing the same thing to each side. | do the same to each side |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A team had some points, then scored 14 more and has 40. Solve y + 14 = 40.
- Subtract 14 from both sides: y + 14 − 14 = 40 − 14.
- Simplify: y = 26.
- Check: 26 + 14 = 40.
Answer: y = 26 points
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Solve x − 4 = 9. Then explain the step you used.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The variable has added to it, so I from both sides.
- I must do the same thing to both sides because .
- My solution is , and my check shows .
- Addition and subtraction are inverse operations because .
Word bank equationvariableinverse operationsubtractisolatebalanceboth sidessolutioncheckundoProperty of Equality
Watch out!A common mistake
A common mistake is applying the same operation instead of the inverse
Lesson 8.28.2 Small Group · Group 2
Group 2Challenge practice
Learning target I can solve one-step addition and subtraction equations using inverse operations, explain why the method works, and use it on a problem I have not seen before.
Why This Matters This is your challenge small group for Lesson 8.2. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.
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1Complete each step, then write the final answer.
Keep both sides balanced. Solve p − 2.75 = 6.40.
- 1What is done to p? What undoes it?
- 2Add 2.75 to both sides. What is p?
- 3Check: what is 9.15 − 2.75?
Final answer: -
2Complete each step, then write the final answer.
This time the variable is on the right side. Solve 18.6 = y + 7.9. Then explain why the side does not matter.
- 1What is done to y? What undoes it?
- 2Subtract 7.9 from both sides. What is y?
- 3Check: what is 10.7 + 7.9?
- 4Why can we solve it the same way when y is on the right side?
Final answer: -
3Complete each step, then write the final answer.
Solve m + 4.8 = 12.3.
Show your workFinal answer: -
4Complete each step, then write the final answer.
Solve 45 = k − 17.
Show your workFinal answer: -
5Complete each step, then write the final answer.
A pug weighs 32 pounds less than a bulldog. The pug weighs 19 pounds. Write and solve an equation to find the bulldog's weight b.
Show your workFinal answer: -
6Complete each step, then write the final answer.
Ana and Ben solve x + 9.5 = 20. Ana gets 10.5. Ben gets 29.5. What is x?
Show your workFinal answer: