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Equation Architect

You finished the unit test -- now it is time to explore, create, and have fun with equations and inequalities. No scores, no pressure. Just mathematical creativity.

6.AT.C.8 · 6.AT.C.8 · 6.AT.C.9 Creative Exploration
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Extra examples, word banks, and sentence starters

🟠 Level 0 — Extra Support

Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
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Design Your Scenario

Become an Equation Architect

You are the architect. Think of a real-world situation that involves an unknown quantity -- something you might wonder about, measure, or figure out. Then model it with an equation or inequality.

Need ideas? Think about everyday situations where you do not know a number yet:
money saved pieces of pizza miles walked hours of sleep points scored books read songs on playlist
Example: "I want to buy a video game that costs $45. I already saved $20. How much more do I need?"
1 Describe your situation

What is happening? Paint a picture with words.

2 What is the unknown? Name your variable.
A variable is a letter that stands for the number you do not know yet. You can pick any letter! Example: "Let m = the amount of money I still need."

Choose a letter and explain what it stands for.

3 Write your equation or inequality
Equation uses = (equal sign). Inequality uses <, >, ≤, or ≥. Example: 20 + m = 45   or   x + 5 > 12

Use your variable from Step 2.

4 Solve it and explain what the answer means
Sentence starter: "I solved my equation by ___. The answer is ___ = ___. This means that in my situation, ___."

Show your thinking and connect the answer back to your story.

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Equation Art Gallery

Walk through the museum of equation stories

Welcome to the gallery! Click through four equation stories. Each one shows a real-world scenario, the equation that models it, and a "What If?" question to stretch your thinking.

Exhibit 1 of 4

The Pizza Party Problem

Marcus is ordering pizza for his class party. Each pizza has 8 slices and there are 24 students who each want at least 2 slices. How many pizzas does he need?

8p = 48
Solution: p = 6. Marcus needs 6 pizzas. Each pizza gives 8 slices, and 6 × 8 = 48 slices total -- enough for 24 students to each get 2.
What if? What if 4 more students joined the party? How would the equation change? What if each pizza had 10 slices instead of 8?
$
Exhibit 2 of 4

The Savings Goal

Amara has $35 saved and wants to buy a skateboard that costs $89. She earns $9 per hour babysitting. How many hours does she need to work?

35 + 9h ≥ 89
Solution: 9h ≥ 54, so h ≥ 6. Amara needs to work at least 6 hours. After 6 hours she earns $54, giving her 35 + 54 = $89 -- exactly enough!
What if? What if Amara already had $50 saved? How would that change the number of hours? What if the skateboard went on sale for $71?
Exhibit 3 of 4

Track Practice

Jayden runs 3 laps every morning. After practice, his coach says he has run a total of 15 laps this week. How many days has he practiced so far?

3d = 15
Solution: d = 5. Jayden has practiced for 5 days. Since 3 × 5 = 15, that accounts for all 15 laps.
What if? What if Jayden wanted to run more than 20 laps this week? Write an inequality for how many days he would need. What if he ran 4 laps per day instead?
Exhibit 4 of 4

The Garden Project

Ms. Rivera's class is planting a school garden. They have 36 seed packets and want to plant them equally in rows. Each row needs at least 4 packets but no more than 9. How many rows could they make?

4 ≤ 36 ÷ r ≤ 9
Solution: If each row gets 4 packets: 36 ÷ 4 = 9 rows. If each row gets 9 packets: 36 ÷ 9 = 4 rows. So they could make 4, 6, or 9 rows (r = 4, 6, or 9, since 36 must divide evenly).
What if? What if they got 12 more seed packets? How many row arrangements would be possible then? What if each row needed exactly 6 packets?

Which exhibit was your favorite? Pick one and explain what you liked about it.

Sentence starters: "I liked this exhibit because..." / "The equation was interesting because..." / "I could relate to this scenario because..."
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The "What If?" Lab

Explore how equations change

Experiment time! Build an equation and then change the numbers to see how the solution changes. There are no wrong answers here -- just discovery.

Choose an equation type, then use the sliders to change the numbers. Watch what happens to the solution!

Coefficient (a) 3
Constant (b) 5
Result (c) 17
Think about it: What happens to x when you make the coefficient (a) bigger? Does x get bigger or smaller?

Your observations: What patterns did you notice while experimenting?

Sentence starters: "When I increased the coefficient, x got..." / "I noticed that when the constant was bigger..." / "The solution changed because..."
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Reflection Journal

Look back on what you learned

Take a moment to think about your journey through Unit 8: Equations and Inequalities. Write honestly -- this is your personal reflection.

What did you learn about equations and inequalities in this unit?
Think about: What is an equation? What is an inequality? How do you solve them? What strategies helped you? "Before this unit, I thought equations were... Now I know that..."
Where do you see equations in your daily life?
Think about: Shopping, cooking, sports, time management, games, sharing things equally. "I use equations when I..." / "Equations show up in my life when..."
What is one thing about equations or inequalities that you want to remember?
This could be: A strategy, a vocabulary word, a trick that helped you, something surprising, or advice you would give a friend. "One thing I never want to forget is..." / "My biggest takeaway is..."