Problem 3 · Steve’s Big DigPrint one blank worksheet now, download its PDF, or prepare a family or classroom packet.

MathJewels.com

Name

Date

Steve’s Big Dig

Complete to collectWhite OpalLevel 2 · 3 Glints

In Minecraft, Steve digs a cube-shaped hole. The hole is 5 blocks long, 5 blocks wide, and 5 blocks deep.

Think about the hole as equal horizontal layers.

Your challenges

How many blocks does Steve remove?
On average, 1 out of every 10 blocks contains coal. How many coal blocks should Steve expect to find in the hole?

Show your answer

Show an equation for each part. If an expected amount is not a whole number, explain what it means. Record both equations and the explanation on separate paper.

Theme

Minecraft

Skills

Helpful first

Grade

Grade 5

Math area

Topics

Math readiness

Designed for Grade 5

Uses Middle Grade 5 math.

Thinking

Standard challenge

The solver chooses and coordinates familiar methods.

Time & response

About 2.5–6.5 minutes

Light amount of written work · Short Explanation response.

How to support: The layer picture supports volume; discuss why an expected amount need not describe one literal hole.

Precise MJD coordinates, factor scores, skill weights, calibration evidence, and curriculum crosswalks. This reference is available to everyone and is intentionally last.

Content level

MJ 5.6

Grades 3–5

Grade 5 progression · point 6

Likely range: MJ 5.0–5.6
Confidence: 82%

Challenge

C2 · Standard

The solver chooses and coordinates familiar methods.

Method selection1
Reasoning depth2
Novelty1
Constraint management1
Proof or justification2

Workload

W1 · Light

A short response with only a few steps.

Active time: 2.5–6.5 minutes · typically 4
Response: Short Explanation
Known-method steps: 4

Mechanical execution1
Written output1
Representation production1
Bookkeeping0

Learning focus

Skills this problem practices

What a successful response demonstrates, with each skill’s share of the content rating.

Find rectangular-prism volume using multiplication formulas
The learner can find rectangular-prism volume using multiplication formulas. This capability is distinct from mere exposure to or isolated use of unit cubes; multiplication.
- Independent mastery
- 25% focus
- MJ 5.2 milestone
Find one tenth of a quantity
The learner can find one tenth of a quantity. The capability is credited only when the task makes that demand necessary for success.
- Independent mastery
- 25% focus
- MJ 5.0 milestone
Interpret a non-whole expected value
The learner can interpret a non-whole expected value. The capability is credited only when the task makes that demand necessary for success.
- Independent mastery
- 50% focus
- MJ 5.6 milestone

Readiness

Helpful prerequisites

Skills the rating assumes are already available to the learner.

Interpret a product as equal groups or a rectangular array
The learner can interpret a product as equal groups or a rectangular array. This capability is distinct from mere exposure to or isolated use of Grade 2 arrays.
- Fluent readiness
- Required
- MJ 3.4 milestone
Find rectangular-prism volume using multiplication formulas
The learner can find rectangular-prism volume using multiplication formulas. This capability is distinct from mere exposure to or isolated use of unit cubes; multiplication.
- Independent readiness
- Required
- MJ 5.2 milestone
Find one tenth of a quantity
The learner can find one tenth of a quantity. The capability is credited only when the task makes that demand necessary for success.
- Independent readiness
- Required
- MJ 5.0 milestone

External alignment

Curriculum and standards crosswalks

Approved evidence-backed locations that support discovery. They do not define the MathJewels rating.

Bridges in Mathematicsthird-edition · 9 locations

Modules6 locations · Representative: Module 1: Multiplication & Volume

Module 1: Multiplication & Volume
grade-5-unit-1-module-1
The official publisher correlation lists this curriculum location for 5.MD.C.5a, 5.MD.C.5b, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 5 Correlations to the Common Core State Standards · Page 15, standard 5.MD.C.5a: Unit 1, Module 1, Sessions 5
- Bridges & Number Corner Third Edition: Grade 5 Correlations to the Common Core State Standards · Page 15, standard 5.MD.C.5b: Unit 1, Module 1, Sessions 5
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 2: Factors, Multiples & Properties
grade-5-unit-1-module-2
The official publisher correlation lists this curriculum location for 5.MD.C.5a, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 5 Correlations to the Common Core State Standards · Page 15, standard 5.MD.C.5a: Unit 1, Module 2, Sessions 1, 2
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 3: Volume
grade-5-unit-6-module-3
The official publisher correlation lists this curriculum location for 5.MD.C.5a, 5.MD.C.5b, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 5 Correlations to the Common Core State Standards · Page 15, standard 5.MD.C.5a: Unit 6, Module 3, Sessions 1, 2
- Bridges & Number Corner Third Edition: Grade 5 Correlations to the Common Core State Standards · Page 15, standard 5.MD.C.5b: Unit 6, Module 3, Sessions 1, 2, 3, 4, 5
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 1: Investigating Solar Energy
grade-5-unit-8-module-1
The official publisher correlation lists this curriculum location for 5.MD.C.5b, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 5 Correlations to the Common Core State Standards · Page 15, standard 5.MD.C.5b: Unit 8, Module 1, Sessions 5, 6
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 2: Investigating Passive Solar Design
grade-5-unit-8-module-2
The official publisher correlation lists this curriculum location for 5.MD.C.5b, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 5 Correlations to the Common Core State Standards · Page 15, standard 5.MD.C.5b: Unit 8, Module 2, Sessions 2
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 3: Designing Solar Homes
grade-5-unit-8-module-3
The official publisher correlation lists this curriculum location for 5.MD.C.5b, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 5 Correlations to the Common Core State Standards · Page 15, standard 5.MD.C.5b: Unit 8, Module 3, Sessions 3
- Partial
- Develops
- Overlapping
- Medium Confidence

Number Corner workouts3 locations · Representative: September: Calendar Collector

September: Calendar Collector
grade-5-number-corner-september-calendar-collector
The official publisher correlation lists this curriculum location for 5.MD.C.5a, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 5 Correlations to the Common Core State Standards · Page 15, standard 5.MD.C.5a: Number Corner September, Calendar Collector
- Partial
- Develops
- Overlapping
- Medium Confidence
January: Solving Problems
grade-5-number-corner-january-solving-problems
The official publisher correlation lists this curriculum location for 5.MD.C.5a, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 5 Correlations to the Common Core State Standards · Page 15, standard 5.MD.C.5a: Number Corner January, Solving Problems
- Partial
- Develops
- Overlapping
- Medium Confidence
April: Calendar Grid
grade-5-number-corner-april-calendar-grid
The official publisher correlation lists this curriculum location for 5.MD.C.5a, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 5 Correlations to the Common Core State Standards · Page 15, standard 5.MD.C.5a: Number Corner April, Calendar Grid
- Partial
- Develops
- Overlapping
- Medium Confidence

Common Core State Standards for Mathematics2010 · 4 locations

Standards1 location · Representative: (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
CCSS.MATH.CONTENT.HSS-MD.A.2
S-MD.A.2 explicitly requires interpreting expected value as the mean of a probability distribution, including values that need not be possible single-trial outcomes.
- Strong
- Assesses
- Narrower
- Independent
- High Confidence

Standard components3 locations · Representative: Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
CCSS.MATH.CONTENT.4.NF.B.4.B
4.NF.B.4b interprets a unit-fraction multiple of a whole number; finding one tenth of a quantity is the case with unit fraction 1/10.
- Strong
- Assesses
- Narrower
- Independent
- High Confidence
Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
CCSS.MATH.CONTENT.5.MD.C.5.A
Find rectangular-prism volume using multiplication formulas was reviewed against CCSS.Math.Content.5.MD.C.5a. The ontology's CCSS locator 5.MD.C.5a-b resolves to this component; the atomic skill is overlapping relative to the published expectation.
- Partial
- Assesses
- Overlapping
- Independent
- Medium Confidence
Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
CCSS.MATH.CONTENT.5.MD.C.5.B
Find rectangular-prism volume using multiplication formulas was reviewed against CCSS.Math.Content.5.MD.C.5b. The ontology's CCSS locator 5.MD.C.5a-b resolves to this component; the atomic skill is overlapping relative to the published expectation.
- Partial
- Assesses
- Overlapping
- Independent
- Medium Confidence