5.NF.B.4 Lesson 1-2-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.2 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

quantity · relationship · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — Make sense, plan, check
1When we do math, we make sense of problems, develop a solution plan, check our progress, and try other strategies when we come to dead ends.
  • The book opens with two warm-ups: about how many peas are in the picture, and decompose 105.76 five different ways. Both are about thinking before computing. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me estimate the peas
  1. A bowl is full of peas — far too many to count one at a time. About how many peas are in the bowl?
  2. I do not count every pea — I look for a group I CAN count, like one small cluster of about 10.
  3. Then I ask how many of those clusters would cover the whole bowl. I count about 12.
  4. 12 clusters of about 10 is 12 × 10 = 120, so my estimate is about 120 peas — a reasoned answer, close enough to be useful.
3Mathematical Word Bank
  • quantity (cantidad) — An amount in a problem — a number with a meaning attached, like 540 meters.
  • relationship (relación) — How two quantities compare or connect to each other.
  • strategy (estrategia) — A plan for how to solve a problem before you start computing.
  • reasonable (razonable) — A solution that makes sense in the context of the problem.
  • persevere (perseverar) — To keep working on a problem, checking your progress and adjusting your plan when you get stuck.
4Watch out
  • Expecting a fraction of a number to be bigger than the number — 5/6 × 540 must be LESS than 540 because 5/6 is less than 1; only a fraction greater than 1, like 6/5, makes the product bigger.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Ana's route is 24 blocks long and she has walked 1/2 of it. Ben's route is 20 blocks and he has walked 3/4 of it. Before you calculate anything: which question do you have to answer to tell who has walked farther?

    1. AHow many blocks each student has actually walked
    2. BWhose whole route is longer
    3. CWhich student started walking first
    4. DHow many blocks Ana still has left
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Ana has walked 1/2 of her 24-block route. How many blocks has she walked?

    1. A12 blocks
    2. B24 blocks
    3. C2 blocks
    4. D48 blocks
    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
  3. 3 MULTIPLE CHOICE

    Ben has walked 3/4 of his 20-block route. How many blocks is that, and who has walked farther — Ana (12 blocks) or Ben?

    1. A15 blocks — Ben has walked farther
    2. B5 blocks — Ana has walked farther
    3. C15 blocks — Ana has walked farther
    4. D16 blocks — Ben has walked farther
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Ben walked 3/4 of his route and Ana walked 1/2 of hers, and Ben did walk farther. Does a bigger fraction ALWAYS mean a longer distance?

    1. ANo — each fraction is of a different route, so you have to compare the actual blocks
    2. BYes — 3/4 is greater than 1/2, so the person with 3/4 always walked farther
    3. CNo — fractions of different numbers can never be compared at all
    4. DYes, but only when both routes are longer than 20 blocks
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 OPEN RESPONSE

    Explain your plan for comparing Ana's and Ben's distances. Use the words we know, we don't know, and my strategy is.

    💬 Sentence Starter: We know ___ .<br>We don't know ___ .<br>My strategy is to ___ , and then ___ .
    ✏️ Mathematical Justification & Response
  2. 6 OPEN RESPONSE

    A third student, Cam, has walked 2/3 of an 18-block route. Work out how far Cam has walked, then place all three students in order. Say what strategy you used.

    💬 Sentence Starter: Cam walked ___ blocks, because ___ .<br>In order from farthest: ___ .<br>My strategy was to ___ .
    ✏️ Mathematical Justification & Response
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

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

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It