Showing What You Know | The Center for Quantitative Studies | Studio Aletheia
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Showing What You Know

Lesson 38 · Benchmark Assessment, Quarter 1 Interim Check

This is your chance to show everything you've learned this quarter, describing data, reasoning about probability, and measuring shapes, all in one sitting. Trust the habits and strategies you've built, and work through each problem carefully.

Focus Demonstrating Q1 mastery: data, probability, area
Accountability Benchmark Assessment + Reflection
Indicator Q1 Interim Benchmark — covering 6.DPSR.1, 6.DPSR.2, 6.MGSR.1.1-1.3
The Center for Quantitative Studies Color Palette Aletheian Green · Aletheian Gold
Learning Targets

Learning Targets and Success Criteria

Today's mini-lesson reviews the full arc of Quarter 1 before you demonstrate what you've learned.

Targets

What I will learn

  • I can demonstrate mastery of describing and displaying data sets.
  • I can demonstrate mastery of probability of simple and complementary events.
  • I can demonstrate mastery of finding area, creating nets, and finding surface area.
  • I can reflect honestly on my strengths and growth areas across the quarter.
Success Criteria

What success looks like

  • I can complete data description problems accurately and independently.
  • I can complete probability problems accurately and independently.
  • I can complete area, net, and surface area problems accurately and independently.
  • I can identify at least one strand I want to strengthen going forward.
Q1 Benchmark: 6.DPSR.1, 6.DPSR.2, 6.MGSR.1.1-1.3

Demonstrate mastery of every standard taught in Quarter 1.

Q1 Interim Benchmark Assessment — covering 6.DPSR.1 (describing data sets), 6.DPSR.2 (probability of simple and complementary events), and 6.MGSR.1.1 through 6.MGSR.1.3 (area, nets, and surface area).
Vocabulary

The words we'll use in today's lesson.

These terms will carry through today's mini-lesson, Data Lab, hands-on activity, journal, and exit challenge, and they'll keep coming back all year.

01 · Collect

Sample Size

The number of data values collected from a population to represent it in a data set.

02 · Describe

Median

The middle value of a data set when the values are listed in order.

03 · Describe

Interquartile Range

The range of the middle 50% of a data set, found by subtracting the lower quartile from the upper quartile.

04 · Notice

Outlier

A data value that is far away from the rest of the data set.

05 · Display

Box Plot

A graph that displays a data set's five-number summary using a box and whiskers.

06 · Predict

Probability

A number from 0 to 1 that describes how likely an event is to happen.

07 · Predict

Complementary Event

The event that an outcome will not happen, made up of every outcome not in the original event.

08 · Measure

Area

The amount of flat space a two-dimensional figure covers, measured in square units.

09 · Name

Trapezoid

A four-sided figure with exactly one pair of parallel sides.

10 · Unfold

Net

A two-dimensional pattern that can be folded up to form a three-dimensional figure.

11 · Identify

Prism

A three-dimensional figure with two identical, parallel bases connected by rectangular faces.

12 · Measure

Surface Area

The total area of all the faces of a three-dimensional figure, found by adding up each face's area.

College & Career Connections

Where this shows up in the real world.

Thinking like a mathematician is not just a school skill. It's what people get paid to do every day, in jobs you may not have heard of yet.

Quantitative Careers

Mastery Now Pays Off All Year

Every strand you've mastered this quarter, data, probability, and measurement, becomes a tool you'll reuse for the rest of the year and in careers from data analysis to architecture. Showing what you know today is really showing yourself how ready you are for what comes next.

Mini-Lesson

One Quarter, Three Standards

Today's mini-lesson reviews the full arc of Quarter 1 before you demonstrate what you've learned.

Quarter 1 covered three standards. In 6.DPSR.1, you learned to collect and describe data, paying attention to sample sizeThe number of data values collected from a population to represent it in a data set., finding a data set's medianThe middle value of a data set when the values are listed in order. and interquartile rangeThe range of the middle 50% of a data set, found by subtracting the lower quartile from the upper quartile., watching for an outlierA data value that is far away from the rest of the data set., and displaying it all on a box plotA graph that displays a data set's five-number summary using a box and whiskers..

In 6.DPSR.2, you learned that probabilityA number from 0 to 1 that describes how likely an event is to happen. describes how likely an event is, and that every event has a complementary eventThe event that an outcome will not happen, made up of every outcome not in the original event.. Then in 6.MGSR.1, you moved into measurement and geometry: finding the areaThe amount of flat space a two-dimensional figure covers, measured in square units. of shapes like the trapezoidA four-sided figure with exactly one pair of parallel sides., creating a netA two-dimensional pattern that can be folded up to form a three-dimensional figure. for a prismA three-dimensional figure with two identical, parallel bases connected by rectangular faces. or pyramid, and using that net to find surface areaThe total area of all the faces of a three-dimensional figure, found by adding up each face's area..

Every one of those skills leaned on the same five habits mathematicians use everywhere: making sense of problems, connecting ideas, communicating clearly, checking reasoning, and finding patterns. Today, you'll show what you know across all three standards, one careful problem at a time.

Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.

Check for Understanding · CFU 1
Before you begin, name one standard from this quarter, DPSR.1, DPSR.2, or MGSR.1, that you feel most confident about, and one you want to double-check your work on.
Toolkit

Materials for the Data Lab.

  • A. Your Data Journal
  • B. Ruler
  • C. Grid paper
  • D. A calculator (if allowed)
  • E. A quiet, focused space
Non-negotiable routine

For every benchmark problem: read carefully, identify which standard it's testing, solve using a strategy you trust, then check your answer before moving on.

Guided Practice

Diagnostic Warm-Up

Before the benchmark, this quick warm-up helps you diagnose which strand needs one more check.

Data Lab
Each option below is a quick diagnostic problem from a different standard; work through one from each strand.
1 · Diagnose
Choose a problem above. Which standard does it test, and how confident do you feel about it?
2 · Practice
Solve the problem, showing your full strategy.
3 · Check
Check your answer using a second method or estimate.
4 · Reflect
What's one thing you'll remind yourself of during the benchmark for this standard?
Hands-On

Benchmark Assessment

Complete the Quarter 1 interim benchmark, showing your best work on every problem.

1
Read: Read each problem carefully before starting, noting which standard it covers.
2
Solve: Show your complete strategy and work for every problem.
3
Check: Review your answers before submitting, checking for reasonableness.
4
Reflect: After submitting, reflect on which standard felt strongest and which needs more review.
Required

Data Journal Entry

Which Mathematical Process Standard did you rely on most today — Problem Solving, Connections, Representation & Communication, Analyze & Justify, or Structure & Patterns? Give one specific example from your Data Lab or hands-on work.
Checklist

Accountability Checklist

Required · Exit Challenge

What Will You Focus On Next Quarter?

Reflect on your benchmark performance. Name one standard, and one vocabulary term like surface area or probability, you want to strengthen next quarter.

Lesson 38 · Benchmark Assessment, Quarter 1 Interim Check

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