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Problem Solving for the 21st Century: Built for the Common Core

Ladybugs and Crickets

Ben has 9 ladybugs and 5 crickets in his jar. Jill has 8 ladybugs and 7 crickets in her jar. Dad thinks they have the same amount of insects in each jar. Is Dad correct? Show and tell how you know.

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assessment
Domain:
Aligned Standard:
Mathematical Practices:
  • MP.1
  • MP.1

    Make sense of problems and persevere in solving them.

  • MP.3
  • MP.3

    Construct viable arguments and critique the reasoning of others.

  • MP.4
  • MP.4

    Model with mathematics.

  • MP.6
  • MP.6

    Attend to precision.

View all Grade 1 tasks

Plan

Underlying Mathematical Concepts

  • Number sense to 15
  • Counting on/Addition
  • Comparison

Possible Problem-Solving Strategies

  • Model (manipulatives)
  • Diagram/Key
  • Tally chart
  • Chart
  • Number line

Formal Mathematical Language and Symbolic Notation

  • Model
  • Diagram/Key
  • Tally chart
  • Chart
  • Number line
  • Total/Sum
  • Amount
  • Addend
  • Per
  • More than (>)/Greater than (>)/Less than (<)
  • Equivalent/Equal to
  • Odd/Even
  • Rule
  • Equal share
  • Odd + Odd = Even
  • Even + Even = Even
  • Odd + Even = Odd
  • Dozen
  • Combinations
  • Sets

A student may independently select a printed number line, number chart, ten frames, graph paper, etc. as they work on a task.

Download printable resources for student representations.

Suggested Materials

Engagement Image:

Teachers may project the images below to launch this task for their students, define nouns, promote discussion, access prior knowledge, and inspire engagement and problem solving.

Click image to enlarge

Click image to enlarge

Task-Specific Evidence

This task requires students to understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s).

Printer-Friendly Planning Sheet
Printer-Friendly Exemplars Rubric

Possible Solutions

  • Task Solution (active tab)
Task Solution

No, Dad is not correct.

Possible Connections

Below are some examples of mathematical connections. Your students may discover some that are not on this list.

  • Ben and Jill have a total of 17 ladybugs.
  • Ben and Jill have a total of 12 crickets.
  • 12 crickets is a dozen.
  • Both Ben and Jill found an odd number of crickets.
  • Ben found the most ladybugs.
  • Jill found the most crickets.
  • Jill found 1 more insect than Ben.
  • Ben found an even total of insects: Odd + Odd = Even.
  • Jill found an odd total of insects: Even + Odd = Odd.
  • Relate to a similar task and state a math link.
  • Solve more than one way to verify the answer.
  • Other combinations are shown for 14 and 15.
  • There are no equal sets of ladybugs or crickets per jar.
Printer-friendly Anchor Paper & Scoring Rationales

Assess

Printer-Friendly Exemplars Rubric

Novice

1

Apprentice

1

Practitioner

1
2

Expert

1

Novice

This student does not meet the standard.

Novice 1

Scoring Rationale

Problem Solving

Apprentice

The student's strategy of diagramming the ladybugs and crickets Ben and Jill have in their jars works to solve part of the task. The student's answer, "NO," is not correct because it is based on comparing nine ladybugs to eight ladybugs and not the total number of insects in each jar.

Reasoning & Proof

Apprentice

The student shows some correct reasoning of the underlying concepts of the task. The student diagrams the correct number of ladybugs and crickets in each jar. The student does not demonstrate understanding that a comparison of the total of insects per jar has to be considered.

Communication

Novice

The student does not use any mathematical language to communicate their reasoning and proof.

Connections

Novice

The student does not make a mathematically relevant observation about their solution.

Representation

Practitioner

The student's diagram is appropriate to the task and accurate. A key defines the ladybugs and crickets and the total numbers of insects in each jar is correct.

Overall Achievement Level:

Novice

Apprentice

This student does not meet the standard.

Apprentice 1

Scoring Rationale

Problem Solving

Apprentice

The student's strategy of diagramming the ladybugs and crickets Ben and Jill have in their jars would work to solve the task. The student omits one cricket from Jill's jar, which leads to an incorrect answer, "Yes."

Reasoning & Proof

Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student understands that a total number of insects in each jar needs to be determined and the two totals compared to determine if Dad is correct. Omitting one cricket from Jill's jar is considered a careless error and not a flaw in the student's reasoning.

Communication

Practitioner

The student correctly uses the mathematical terms diagram, key, more than.

Connections

Practitioner

The student makes the mathematically relevant observation, "I know Ben has one more ladybug than Jill because he has nine ladybugs and she has eight ladybugs."

Representation

Apprentice

The student's diagram is appropriate to the task but is not accurate. The seventh cricket is missing from Jill's jar. A key defines the ladybugs, crickets, and jars.

Overall Achievement Level:

Apprentice

Practitioner

This student meets the standard.

Practitioner 1

Scoring Rationale

Problem Solving

Practitioner

The student's strategy of diagramming the ladybugs and crickets Ben and Jill have in their jars, finding the total number of insects per jar, and comparing the totals to see if Dad is correct, works to solve the task. The student's answer, "A: no," is correct.

Reasoning & Proof

Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student understands that a total number of insects in each jar needs to be determined and the two totals compared to determine if Dad is correct.

Communication

Practitioner

The student correctly uses the mathematical terms diagram, key, more than.

Connections

Practitioner

The student makes the mathematically relevant observations, "Jill has one more bug than Ben," and, "14 + 15, 10 + 10 + 9 = 29 bugs in all."

Representation

Practitioner

The student's diagram is appropriate to the task and accurate. A key defines the ladybugs, crickets, and jars. Each jar contains the correct number of each insect.

Overall Achievement Level:

Practitioner

This student meets the standard.

Practitioner 2

Scoring Rationale

Problem Solving

Practitioner

The student's strategy of using a number line to indicate the ladybugs and crickets Ben and Jill have in their jars, finding the total number of insects per jar, and comparing the totals to see if Dad is correct, works to solve the task. The student's answer, "A-no," is correct.

Reasoning & Proof

Practitioner

The student shows correct reasoning of the underlying concepts of the task. The student understands that a total number of insects in each jar needs to be determined and the two totals compared to determine if Dad is correct.

Communication

Practitioner

The student correctly uses the mathematical term amount from the task. The student also correctly uses the terms number line, more.

Connections

Practitioner

The student makes the mathematically relevant observations, "They don't have the same amount of each bug," "Ben has more ladybugs," "Jill has more crickets," and, "Jill has 1 more bug."

Representation

Practitioner

The student's number line is appropriate to the task and accurate. All necessary labels are indicated and the student's "jumps" are correct.

Overall Achievement Level:

Practitioner

Expert

,
This student exceeds the standard.

Expert 1

Scoring Rationale

Problem Solving

Expert

The student's strategy of using a diagram to indicate the ladybugs and crickets Ben and Jill have in their jars, finding the total number of insects per jar, and comparing the totals to see if Dad is correct, works to solve the task. The student's answer, "Dad is rong," is correct. The student verifies that their answer is correct by using a new strategy of a tally chart. The student also applies the rules for addition with even and odd numbers.

Reasoning & Proof

Expert

The student shows correct reasoning of the underlying concepts of the task. The student understands that a total number of insects in each jar needs to be determined and the two totals compared to determine if Dad is correct. The student uses a tally chart to verify that their answer is correct and also applies the addition rules using odd and even numbers.

Communication

Expert

The student correctly uses the mathematical terms key, diagram, more than, less than, more, tally, chart, odd, even, rules, addend, sum. The student correctly uses the notation "O + O = E" and "E + O = O" and defines the O (odd) and E (even) in the scribing.

Connections

Expert

The student makes the mathematically relevant Practitioner observations, "I see that Ben has one more ladybug than Jill," "I see that Ben has two less crickets than Jill," and, "I see Jill has one more insect in her jar." The student makes the Expert connection by using a tally chart to verify that the student's answer is correct. The student states, "I used the same key for the ladybug and crickets. I got fourteen and fifteen again so I am correct. I proved it didn't I!" The student uses the odd and even rules. 9 + 5 = 14, O + O = E, 8 + 7 = 15, E + O = O. The student states, "I did O for Odd and E for Even. If you know them you know the answer is no."

Representation

Expert

The student's diagram is appropriate and accurate. All necessary labels are included. The student's tally chart is appropriate and accurate. All necessary labels are included and supported by the student's text. The student compares their tally chart to their diagram to verify that their answer is correct.

Overall Achievement Level:

Expert

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