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

Planting Seeds

Luke is planting seeds in pots. Luke has eighty-four seeds. Luke wants to have the same number of seeds in each pot. Luke does not want to plant more than fourteen seeds in each pot. Luke only has twenty-five pots. What are three ways Luke can plant the same number of seeds in each pot? Show all your mathematical thinking.

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instructional
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 3 tasks

More Accessible Version

Luke is planting seeds in pots. Luke has 60 seeds. Luke wants to have the same number of seeds in each pot. Luke does not want to plant more than 10 seeds in each pot. Luke only has 18 pots. What are two ways Luke can plant the same number of seeds in each pot? Show all your mathematical thinking.

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More Challenging Version

Luke is planting seeds in pots. Luke has eighty-four seeds. Luke wants to have the same number of seeds in each pot. Luke does not want to plant more than ten seeds in each pot. Luke only has thirty pots. What are all of the ways Luke can plant the same number of seeds in each pot? Show all your mathematical thinking.

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Plan

Underlying Mathematical Concepts

  • Factors of 84
  • Identifying a division situation
  • Finding a missing factor when the product and one factor are known
  • Partitioning into equal shares
  • Repeated subtraction of equal parts

Possible Problem-Solving Strategies

  • Model (manipulatives)
  • Diagram/Key
  • Table
  • Number line

Formal Mathematical Language and Symbolic Notation

  • Model
  • Diagram/Key
  • Table
  • Number line
  • Factors
  • Product
  • Quotient
  • Divisor
  • Dividend
  • Array
  • Greater than (>)/Less than (<)
  • Equivalent/Equal to
  • Sets/Groups
  • Total/Sum
  • Amount
  • Odd/Even
  • Most/Least
  • Remainder
  • Dozen
  • Combinations/Arrangements
  • Commutative Property

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 the meaning of division: If I know the whole (84 seeds) and the number of seeds in each pot I can divide to find the number of pots. Or, if I know the whole (84 seeds) and the number of pots, I can divide to find the number of seeds in each pot.

Printer-Friendly Planning Sheet
Printer-Friendly Exemplars Rubric

Possible Solutions

  • Task Solution (active tab)
  • More Accessible Solution
  • More Challenging Solution
Task Solution

Luke can plant the following: 6 pots with 14 seeds in each, 7 pots with 12 seeds in each, 12 pots with 7 seeds in each, 14 pots with 6 seeds in each, 21 pots with 4 seeds in each.

More Accessible Solution

Luke can plant the following: 15 pots with 4 seeds in each, 12 pots with 5 seeds in each, 10 pots with 6 seeds in each, 6 pots with 10 seeds in each.

More Challenging Solution

Luke can plant the following: 28 pots with 3 seeds in each, 21 pots with 4 seeds in each, 14 pots with 6 seeds in each, 12 pots with 7 seeds in each.

Possible Connections

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

  • Luke cannot use all 25 pots because 84 ÷ 25 gives a remainder.
  • More than 3 ways are shown to plant the seeds.
  • There are 12 combinations if Luke could use 84 pots and 84 seeds.
  • Solve more than one way to verify the answer.
  • Relate to a similar task and state a math link.
  • The most pots Luke can use is 21.
  • The least number of seeds in each pot is 4.
  • 84 seeds is 7 dozen.
  • 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84 are factors of 84.

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