Student Name

Period

Date

Mission 7 · Unit 3

Percent Reasoning

6.RP.A.3.C · Unit 3

Today's objective: Find a percent of a quantity and solve percent problems.

Need a hint?

Re-read the problem and underline the numbers and the question. Pick one representation (model, table, or equation), show your steps, and check that your answer makes sense for the situation.

The sixth-grade student council is planning a school supplies drive. They surveyed 250 students about which supplies they need most. The results show that 35% need notebooks, 22% need pencils, 18% need folders, 15% need erasers, and 10% need glue sticks. Your team must convert every percentage to a fraction and a decimal, calculate the exact number of students in each category, verify the total, and recommend how to split a $500 donation budget across the five supply categories proportionally.

Team Roles

Facilitator Reads the survey scenario aloud, ensures every team member converts at least one percent before the group compares results, and monitors the timer.

Model Builder Creates the fraction-decimal-percent conversion table, draws a bar model or circle graph to represent the survey data, and labels all three forms.

Precision Checker Verifies that all five percentages add to 100%, confirms each student count is a whole number, and checks the budget splits sum to exactly $500.

Reporter Prepares the defense: states the budget recommendation, shows conversion evidence, and explains one rounding decision the team made.

Investigation

The Problem

A survey of 250 sixth graders found that students need five types of school supplies. The results are expressed as percents:

Notebooks: 35%
Pencils: 22%
Folders: 18%
Erasers: 15%
Glue Sticks: 10%

Your tasks:

Convert each percent to a fraction (simplify!) and a decimal.
Calculate the exact number of students for each category.
Verify that the five student counts add up to 250.
Split a $500 donation budget proportionally based on the survey percentages.
Create a visual model (bar model, pie chart, or number line) that shows how the five categories compare.

Step-by-Step Investigation Guide

Verify the percents add to 100% Before converting anything, add: 35 + 22 + 18 + 15 + 10. If the sum is not 100%, something is wrong with the data.
Why must survey percents always add to exactly 100%?
Convert each percent to a fraction Write the percent over 100, then simplify. Example: 35% = 35/100 = 7/20. Find the GCF of the numerator and 100 to simplify.
Which of the five percents produces the simplest fraction? Which is hardest to simplify?
Convert each fraction to a decimal Divide the numerator by the denominator. Example: 7 / 20 = 0.35. Check: does the decimal make sense compared to the percent?
How can you check your decimal without a calculator? (Hint: think about equivalent fractions with denominator 10 or 100.)
Calculate the number of students per category Multiply each decimal by 250. Example: 0.35 x 250 = 87.5. Wait -- can you have half a student? Discuss how to handle non-whole results.
If 0.35 x 250 = 87.5, does the survey data make perfect sense for exactly 250 students? What does this tell you about rounding in surveys?
Calculate the budget allocation Apply each percent to $500. Example: 35% of $500 = 0.35 x 500 = $175. Check that all five amounts add to exactly $500.
Why is it important that the budget allocations add to exactly $500? What happens if they do not?
Build a visual model and prepare your defense Create a bar model, pie chart, or stacked number line that shows all five categories with fraction, decimal, AND percent labels. Write a one-sentence recommendation for how to spend the $500.
Which visual model makes it easiest for another student to compare the five categories at a glance?

Percent Calculator Tool

Enter a percent and a total to find the part. Use this to check your work.

Percent: % of = 87.5

As a fraction: 7/20

As a decimal: 0.35

Visual Bar Model

Notebooks

35%

Pencils

22%

Folders

18%

Erasers

15%

Glue

10%

Language Support

Key Vocabulary

Percent: A number out of 100 (per = for each, cent = hundred)

Fraction: A part of a whole written as numerator over denominator

Decimal: A number written with a dot to show parts less than one

Convert: Change from one form to another (same value, different look)

Proportional: Keeping the same ratio when numbers change size

Survey: Asking many people a question and recording answers

Budget: A plan for how to spend a set amount of money

Simplify: Reduce a fraction to its smallest form (divide top and bottom by GCF)

Sentence Frames

"___% means ___ out of every 100, which equals the fraction ___."
"To convert ___% to a decimal, I divide by 100 and get ___."
"___% of 250 students is ___ students because ___ x 250 = ___."
"The budget for ___ should be $___ because it is ___% of $500."

Multiple Representations

Conversion Table

Organize all five items in rows with columns for percent, fraction, decimal, students, and budget.

Bar / Strip Model

One long bar = 100%. Divide it into sections proportional to each category.

Pie / Circle Graph

Divide a circle into five sectors. Label each with all three forms.

Double Number Line

Top line shows percents 0-100. Bottom line shows student counts 0-250.

Timed Lab Phases

Explore phase

Click a phase, then press Start.

04:00

Read the survey scenario aloud. Assign roles. Underline the five percentages, the total (250), and the budget ($500). Confirm that the percents add to 100%.

What are the three forms we need to show for each percent? Why does each form matter?

Checkpoint: every team member can name all five categories and their percents from memory.

Model Builder creates the conversion table. Each team member converts at least one percent to a fraction (simplified) and a decimal. Then calculate the number of students for each category (decimal x 250).

Which conversions produce terminating decimals and which do not? Why?

Checkpoint: table has all 5 rows filled. Student counts are calculated. Precision Checker has verified the fraction simplifications.

Calculate the budget allocation for each category: decimal x $500. Verify the total is exactly $500. Build the visual model. Discuss: does 87.5 students make sense? How should you handle that?

If you round each student count, will they still add to 250? What is the rounding dilemma?

Checkpoint: budget splits verified, visual model started, and team has discussed the rounding issue.

Reporter prepares the presentation. Show the conversion table, the visual model, and the budget recommendation. Explain why your team chose to round the way you did.

What is one error your team caught during the checking process?

Checkpoint: Reporter can explain conversions, budget splits, and the rounding decision in under 90 seconds.

Extension Challenge

The student council discovers that 12 students changed their answer from pencils to notebooks. Recalculate the new percentages for notebooks and pencils. Express each new percent as a fraction and decimal. How does this change the budget allocation?

"What If?" Variations

the survey had 400 students instead of 250? Would all the student counts be whole numbers now?
glue sticks jumped from 10% to 25% and notebooks dropped to 20%? Recalculate the budget.
you had to express 22% as a fraction with denominator 200? What would the numerator be?

Real-Life Connection

Businesses use percent reasoning every day to read survey results, set prices with discounts, calculate sales tax, and allocate budgets. When a store says "30% off," they are doing the same fraction-decimal-percent conversion your team just practiced.

Defense Preparation

Defense Questions

Show the fraction and decimal form for each of the five percentages. How did you simplify each fraction?
How many students chose each supply? Show your multiplication.
How should you handle a result like 87.5 students? Explain the rounding challenge.
What is the budget allocation for each category? Prove they sum to $500.
Which visual model did your team choose, and why is it the best way to compare five categories?

Sentence Starters for Your Defense

"We converted 35% to the fraction 7/20 by finding the GCF of 35 and 100, which is..."
"To find the number of students, we multiplied ___ by 250 and got..."
"The budget for notebooks is $___ because 0.35 x $500 = ..."
"We handled the rounding problem by..."

What Makes a Strong Defense

Clear Conversions All 5 items shown in fraction, decimal, and percent form

Accurate Calculations Student counts and budget amounts verified with totals

Reasonableness Rounding discussed and visual model supports the argument

Exit Product

Submit a one-page lab note with:

Conversion table: all 5 items with percent, fraction (simplified), and decimal
Student count calculations: decimal x 250 for each category
Budget allocation: decimal x $500 for each category, verified total
Visual model (bar, pie, or number line) with all three forms labeled
One-sentence budget recommendation
Three-sentence defense: claim, evidence, reasonableness check

Work Space

Conversion Table:

Supply	Percent	Fraction	Decimal	Students	Budget
Notebooks	35%
Pencils	22%
Folders	18%
Erasers	15%
Glue Sticks	10%

Total students check: ___ + ___ + ___ + ___ + ___ = ___

Total budget check: $___ + $___ + $___ + $___ + $___ = $___

Visual Model:

Recommendation and Defense: