MPP.3 Lesson 10-1-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

10.1 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

profession · inventory · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — Math is an integral part of nearly every profession
1People use math every day in their professions and their hobbies — and it is a good tool for solving problems around your house, too — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
2Worked Example — Watch me find the math in a chef's day
  1. When chefs plan menus, they determine the number of items on the menu and calculate the price point for each item.
  2. They decide on the portion size of each item and project how much food is needed for each day.
  3. They calculate how much of each ingredient to order — that is counting, measuring, and multiplying, all before a single dish is cooked.
3Second Model — Try it together — then prove it
  1. A planter that is 4 feet long and 2 feet wide has an area of 4 × 2 = 8 square feet — that tells us how many plants fit.
  2. If the soil needs to be 1 foot deep, the volume is 4 × 2 × 1 = 8 cubic feet — that tells us how much soil to buy.
  3. Gardeners also measure seed depth and the distance between seeds. What other garden decisions need math?
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • profession (profesión) — A job someone is trained to do, like chef, nurse, or carpenter.
  • inventory (inventario) — The supply of items a business keeps on hand, tracked by counting.
  • portion (porción) — The measured amount of food served to one person.
  • area (área) — The amount of flat space a surface covers, measured in square units.
  • volume (volumen) — The amount of space something fills, measured in cubic units.
5Watch out
  • Believing math only 'counts' when it happens in a classroom — and walking past the calculating, measuring, and projecting inside jobs, hobbies, and chores every day.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Each person who rinses instead of running water saves 8 gallons a day. Complete the table.

    People in the houseThinkingGallons saved per day
    3
    5
    8
    ✏️ Scratchpad / Reasoning
  2. 2 MATCHING GAME

    Match each person to the math their real-world task uses.

    1. Chef tripling a recipe
    2. Gardener filling a 4 × 2 × 1 ft planter
    3. Family tracking water savings
    4. Shopper comparing two sizes
    • AMultiply every ingredient by 3
    • BVolume: 8 cubic feet of soil
    • C8 gallons × 365 days
    • DUnit rate: price ÷ quantity
  3. 3 MULTIPLE CHOICE

    Which statement matches this lesson's big idea?

    1. AMath is everywhere — in professions, hobbies, and problems around your house
    2. BMath is just a school subject with little relevance outside the classroom
    3. COnly professions like chef use math; hobbies do not
    4. DMath is only useful for people who work with money
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 4 MULTIPLE CHOICE

    Each person saves 2,920 gallons a year. Which correctly compares households of 3, 4, 5, and 8 people?

    1. A8,760 · 11,680 · 14,600 · 23,360 gallons
    2. B8,760 · 11,680 · 14,600 · 20,440 gallons
    3. C2,923 · 2,924 · 2,925 · 2,928 gallons
    4. D8,760 · 11,680 · 14,600 · 46,720 gallons
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 OPEN RESPONSE

    What factors do you consider to determine the number of plants you can put in a planter garden? Is the TYPE of plant a factor? Explain your thinking.

    ✏️ Mathematical Justification & Response
  2. 6 OPEN RESPONSE

    Someone says, 'Math is just a school subject. I'll never use it after class.' Using the chef, the gardener, or the water problem, write what you would say back.

    ✏️ Mathematical Justification & Response
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The mathematical model proves the solution because each step preserves quantitative equivalence.
BUT An estimate provides a quick benchmark, but an exact proof is required for precision.
SO The quantities follow the standard rule, so the final result is verified with certainty.
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It