Grades K–5

Formative Assessment Math Probes written by Cheryl R. Tobey provide you with insight into student thinking.

Deliver insightful instruction today!

Uncover misconceptions to deepen understanding

Math PROBES

Reveal Math K–5 Contributing Author

Cheryl Tobey Math Probes appear in each module of Reveal Math K–5, an elementary core mathematics program. Enjoy these samples and use them in your classroom today.

Learn more about the full Reveal Math program at RevealMath.com

Cheryl R. Tobey is an Author and Educational Consultant. She has been project director for Formative Assessment in the Mathematics Classroom: Engaging Teachers and Students and a mathematics specialist for Differentiated Professional Development: Building Mathematics Knowledge for Teaching Struggling Students. Both projects are funded by the National Science Foundation. Cheryl’s work, including published books, is primarily in the areas of formative assessment and professional development.

MATHPROBES

CHERYL TOBEY

Module 3 • Place Value to 1,000 135

MODULE

3Name

Math ProbeC

opyr

ight

© M

cGra

w-H

ill E

duc

ati

on

Skip Counting on the Number LineCircle the number that belongs in the box on the number line.

Circle the missing number. Explain your thinking.A.

35 40 45

a) 46 c) 50

b) 47 d) 55

B.

505405305

a) 506 c) 510

b) 507 d) 605

RM_G2_M3_SE_MATH_PROBE_3-15-18.indd 135 3/28/18 10:54 AM

TM

RevealMath.com

Gra

de 2

• Pr

obe

1

136 Math Probe • Skip Counting on the Number Line

Math Probe

Copyr

ight

© M

cGra

w-H

ill E

duc

ati

on

MATHPROBES

CHERYL TOBEY

Circle the number that belongs in the box on the number line.

Circle the missing number. Explain your thinking.C.

35 45 55

a) 25 c) 34

b) 30 d) 36

D.

45 47 49

a) 43 c) 40

b) 44 d) 50

RM_G2_M3_SE_MATH_PROBE_3-15-18.indd 136 3/28/18 10:54 AM

136 Math Probe • Skip Counting on the Number Line

Math Probe

Copyr

ight

© M

cGra

w-H

ill E

duc

ati

on

MATHPROBES

CHERYL TOBEY

Circle the number that belongs in the box on the number line.

Circle the missing number. Explain your thinking.C.

35 45 55

a) 25 c) 34

b) 30 d) 36

D.

45 47 49

a) 43 c) 40

b) 44 d) 50

RM_G2_M3_SE_MATH_PROBE_3-15-18.indd 136 3/28/18 10:54 AM

Module 4 • Measure and Compare Lengths 145

MODULE

4Name

Math ProbeC

opyr

ight

© M

cGra

w-H

ill E

duc

ati

on

Comparing Measurements

Which measurement is longer?

Circle both if they are equal in length.

Circle one or both. Explain your choices or answers.

A.

14 inches

2 feet

B.

3 feet

36 inches

RM_G2_M4_SE_MATH_PROBE_3-15-18.indd 145 3/28/18 3:03 PM

TM

RevealMath.com

Gra

de 2

• Pr

obe

2

146 Math Probe • Comparing Measurements

Math Probe

Copyr

ight

© M

cGra

w-H

ill E

duc

ati

on

MATHPROBES

CHERYL TOBEY

Which measurement is longer?

Circle both if they are equal in length.

Circle one or both. Explain your choices or answers.

C.

2 meters

180 centimeters

D.

420 centimeters

4 meters

RM_G2_M4_SE_MATH_PROBE_3-15-18.indd 146 3/28/18 3:03 PM

Teacher Guide Instruction

Math Probe: Skip Counting on the Number Line

Students circle the missing number that belongs in the empty box that is positioned along a given number line. Students justify their answers. Use the probe as an individual interview or in small groups.

Targeted Concept Interpret an interval on a number line and skip count up or back.

Targeted Misconceptions Some students have difficulty determining the interval on a number line and with skip counting by 2s, 5s, 10s, or 100s. Some students may have difficulty sequencing numbers on a number line. In particular, they may not understand that smaller numbers are positioned to the left of larger numbers.

Use the Math Probe to determine potential misconceptions your students may have during this module. To begin, review the probe prior to assigning it.

Probe

PDF

Analyze The Probe Collect and Assess Student WorkIf the student … Then the student likely …

A. circled aB. circled aC. circled cD. circled b

always counts up or back by 1 to determine the missing number, regardless of the interval shown on the number line.

A. circled b or dB. circled b or cC. circled b or dD. circled c or d

skip counts up or back by an amount that is different from that shown by the intervals on the number line.

C. circled dD. circled d

has trouble interpreting that numbers to the left of a number on a number line are smaller, not greater.

142   Module 4 • Place Value to 1,000

Use one of the following resources or suggestions to address students’ misconceptions:

• Use kinesthetic experiences such as creating number lines on your classroom floor and having students walk on them.

• Provide experiences with a variety of number lines with different intervals and different starting and ending labels. Provide both labeled and unlabeled number lines so that students grow to view this tool as flexible rather than fixed and to avoid the overgeneralization that all number lines should look a certain way.

• Use concrete materials such as base-ten blocks to build place-value ideas and to connect those ideas to the number-line representation.

• The number-line representation is a powerful tool for determining the relative magnitude of numbers. Use it to help students build a habit of reasoning about whether their answers make sense.

Revisit the Probe After additional instruction, have students review their initial answers to the probe.

Are there any answers you would like to change? Explain why you might want to change them.

Take ActionStudent Companion, pp. 135–136

Are there any questions that you still have about any of the items on this probe?

Math Probe • Skip Counting on the Number Line   143

Explanations will vary.

Explanations will vary.

2.NBT.A.2

Module 3 • Place Value to 1,000 135

MODULE

3Name

Math Probe

Copyr

ight

© M

cGra

w-H

ill E

duc

ati

on

Skip Counting on the Number LineCircle the number that belongs in the box on the number line.

Circle the missing number. Explain your thinking.A.

35 40 45

a) 46 c) 50

b) 47 d) 55

B.

505405305

a) 506 c) 510

b) 507 d) 605

Explanations will vary.

Explanations will vary.

136 Math Probe • Skip Counting on the Number Line

Math Probe

Copyr

ight

© M

cGra

w-H

ill E

duc

ati

on

MATHPROBES

CHERYL TOBEY

Circle the number that belongs in the box on the number line.

Circle the missing number. Explain your thinking.C.

35 45 55

a) 25 c) 34

b) 30 d) 36

D.

45 47 49

a) 43 c) 40

b) 44 d) 50

TM

RevealMath.com

Gra

de 2

• Pr

obe

1

Math Probe: Comparing Measurements

Students compare two length measurements, each given in a different unit. They circle the greater measurement or circle both measurements if they are equal in length. Students justify their answers.

Targeted Concept Understand that both the number of units (the measure) and the size of the unit of measure must be considered when comparing measurements.

Targeted Misconceptions Some students focus only on the number of units and choose the measurement that has the greater number of units. Some students only consider the greater unit of measure without consideration of the number of those units. Some students may not know the relationship between two units of length in the same system.

Use the Math Probe to determine potential misconceptions your students may have during this module. To begin, review the probe prior to assigning it.

Probe

PDF

Analyze The Probe Collect and Assess Student WorkIf the student … Then the student likely …

A. circled 14 inchesB. circled 36 inchesC. circled 180 centimeters

chooses the greater number of units without taking into account that the unit of measure must also be considered when choosing the greater measurement. Note that the student may apply this misconception to obtain the correct answer for item D.

A. circled 2 feetB. circled 4 meters

chooses the larger unit without considering how many of those units are in the measurement.

B. circled 3 feet or 36 inches, but not       both

does not know the correct relationship between feet and inches or miscalculates; OR may have the misconception that lengths cannot be equal if the numeric values (the measures) are different.

circled a variety of incorrect answers may not know the correct relationship between units or how to express measures in different units.

135   Module 4 • Measure and Compare Lengths

Math Probe: Comparing Measurements

Students compare two length measurements, each given in a different unit. They circle the greater measurement or circle both measurements if they are equal in length. Students justify their answers.

Targeted Concept Understand that both the number of units (the measure) and the size of the unit of measure must be considered when comparing measurements.

Targeted Misconceptions Some students focus only on the number of units and choose the measurement that has the greater number of units. Some students only consider the greater unit of measure without consideration of the number of those units. Some students may not know the relationship between two units of length in the same system.

Use the Math Probe to determine potential misconceptions your students may have during this module. To begin, review the probe prior to assigning it.

Probe

PDF

Analyze The Probe Collect and Assess Student WorkIf the student … Then the student likely …

A. circled 14 inchesB. circled 36 inchesC. circled 180 centimeters

chooses the greater number of units without taking into account that the unit of measure must also be considered when choosing the greater measurement. Note that the student may apply this misconception to obtain the correct answer for item D.

A. circled 2 feetB. circled 4 meters

chooses the larger unit without considering how many of those units are in the measurement.

B. circled 3 feet or 36 inches, but not       both

does not know the correct relationship between feet and inches or miscalculates; OR may have the misconception that lengths cannot be equal if the numeric values (the measures) are different.

circled a variety of incorrect answers may not know the correct relationship between units or how to express measures in different units.

135   Module 4 • Measure and Compare Lengths

Use one of the following resources or suggestions to address students’ misconceptions:

• Revisit the hands-on measuring activities in Lessons 4-3 – 4-8.

• Have students measure the length of objects using two different units (feet and inches or centimeters and meters) to build understanding of the relationship between units of measure, and that an object's length can be expressed in a variety of ways using different units. Emphasize that the length remains the same, but the measurement looks different when different units are used.

• Provide opportunities for students to make estimates of length in order to build visual and spatial understanding of the size of different units of length.

• Use the probe to facilitate discussions to hear student strategies for interpreting and comparing the two given measures of length.

• Reinforce that in order to interpret a measure of length, you need to have both the number of units and a label of the unit of measure.

Revisit the Probe After additional instruction, have students review their initial answers to the probe.

Are there any answers you would like to change? Explain why you might want to change them.

Take ActionStudent Companion, pp. 145–146

Are there any questions that you still have about any of the items on this probe?

Math Probe • Comparing Measurements    136

Explanations will vary.

Explanations will vary.

2.MD.A.2

Module 4 • Measure and Compare Lengths 145

MODULE

4Name

Math Probe

Copyr

ight

© M

cGra

w-H

ill E

duc

ati

on

Comparing Measurements

Which measurement is longer?

Circle both if they are equal in length.

Circle one or both. Explain your choices or answers.

A.

14 inches

2 feet

B.

3 feet

36 inches

Explanations will vary.

Explanations will vary.

146 Math Probe • Comparing Measurements

Math Probe

Copyr

ight

© M

cGra

w-H

ill E

duc

ati

on

MATHPROBES

CHERYL TOBEY

Which measurement is longer?

Circle both if they are equal in length.

Circle one or both. Explain your choices or answers.

C.

2 meters

180 centimeters

D.

420 centimeters

4 meters

TM

RevealMath.com

Gra

de 2

• Pr

obe

2

TM

Reveal Math empowers educators to uncover the mathematician in every student through powerful explorations, rich discourse, and timely and insightful differentiation opportunities.

Learn more at RevealMath.com

Reveal the Full Potential in Every Student.

MA18W13856