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Subjects

- Arts & Humanities

--Language Arts - Mathematics

--Algebra

--Applied Math

--Arithmetic

--Measurement

--Process Skills

Grade

- 3-5
- 6-8
- 9-12

Brief Description

Students put their math thinking in writing with this pumpkin puzzler.

Objectives

Students will

- analyze ways to use math skills to solve a specific problem.
- describe in writing their math thought processes.

Keywords

pumpkin, Halloween, fall, October, September, autumn, jack-o-lantern, math and writing, math process, analyze, problem solving, puzzle

- jack-o'-lantern (optional)
- package of candles (the ideal size is a large birthday candle or a votive candle)
- matches or a cigarette lighter
- glass chimney from a lamp or lantern

Lesson Plan

**Lesson Note**

In order to solve this puzzle activity, it is essential that a candle be burned, but students should not handle the candle or get near it; they will not use matches. The candle should be burned safely surrounded by a glass chimney from a lamp or lantern. * The burning candle should not -- under any circumstances -- be left unattended. Matches and candles should be placed in a locked storage area when not in use.*

** Present the Problem **

Present the following problem to students:

Today is October 10. Halloween is only a few weeks away. You have just carved a jack-o'-lantern from a pumpkin and you want to use a candle to light the pumpkin each night between now and Halloween night on October 31. You will light the pumpkin at 5:00 p.m. each evening and let the candle burn until 10 p.m. each night.You were just looking through the newspaper and saw that a local department store is having a sale on candles. A box of 6 candles is on sale for $3.98. You want to buy the candles, but you want to know how many boxes of candles you will need to light the pumpkin from now through Halloween night.

That is the problem. How will students figure out how many boxes of candles they need? Challenge each student to write a plan of action for solving the problem. Then give them time to share their plans. Chances are some students will share that they want to know how long one candle in the box will burn in order to figure out how many boxes of candles they will need. If that thought is presented -- as it most surely will be -- you will want to set up an "experiment candle." Light the candle and place the glass chimney over it. Place it in a safe place in the classroom and declare that place "Off Limits" to students; post a sign nearby to emphasize that point. Have students record the exact time the candle is lit and monitor it from a distance. When the light of the candle flickers out, students should determine how long it stayed lit. Armed with that information, they will be able to figure out how many boxes of candles they need and how much those candles will cost.

When students have figured out how many boxes of candles they need, ask them to write a paragraph explaining their math thought processes. This might be given as a homework assignment. The next day, ask students to share their responses. Did most students solve the problem in a similar way? Ask them to reveal their thought processes; they will likely have arrived at similar answers in a handful of different ways.

Possible responses:

Students know how long one candle will burn, so they can assume that all the candles in a box will burn for a similar amount of time. With that piece of information, students calculate the number of candles that will be needed to light the pumpkin each evening from October 10 through October 31 (22 days) from 5 p.m. to 10 p.m. each night (5 hours a night).

22 days x 5 hours per day = 110 hours

Students might solve the problem using division. They might divide 110 by the number of hours one candle burns to learn how many candles will be needed. Then they will divide that number by 6 to learn how many boxes of candles will be needed. If the answer is a whole number and a fraction, then students will round up to determine how manyboxesof candles are needed. They multiply that number times the cost of one box of candles ($3.98) to get the total cost.

If you have older students, challenge them to solve the problem algebraically. In that case, they might use a thought process such as this: Ifxequals the number of hours a candle will burn (xis a known number) and 110 is the total number of hours of candle time that will be required, students can solve the problem by using the formulaxxy= 110. Is this x times y? It's confusing as written. That problem can be restated asy= 110 divided byx(xbeing the number of hours the test candle burned). In order to find the total cost, students would roundyup and multiply by $3.98 to determine the total cost. Students might even figure sales tax into their totals.

In what other ways did students arrive at the correct answer?

Assessment

Grade student writing on the completeness of their math detail.

Lesson Plan Source

Education World

Submitted By

Gary Hopkins

National Standards

**LANGUAGE ARTS: English****GRADES K - 12**

NL-ENG.K-12.3 Evaluation Strategies

NL-ENG.K-12.4 Communication Skills

NL-ENG.K-12.7 Evaluating Data

NL-ENG.K-12.12 Applying Language Skills

**MATHEMATICS: Number and Operations****GRADES 3 - 5**

NM-NUM.3-5.1 Understand Numbers, Ways of Representing Numbers, Relationships Among Numbers, and Number Systems

NM-NUM.3-5.2 Understand Meanings of Operations and How They Relate to One Another

NM-NUM.3-5.3 Compute Fluently and Make Reasonable Estimates**GRADES 6 - 8**

NM-NUM.6-8.1 Understand Numbers, Ways of Representing Numbers, Relationships Among Numbers, and Number Systems

NM-NUM.6-8.2 Understand Meanings of Operations and How They Relate to One Another

NM-NUM.6-8.3 Compute Fluently and Make Reasonable Estimates**GRADES 9 - 12**

NM-NUM.9-12.1 Understand Numbers, Ways of Representing Numbers, Relationships Among Numbers, and Number Systems

NM-NUM.9-12.2 Understand Meanings of Operations and How They Relate to One Another

NM-NUM.9-12.3 Compute Fluently and Make Reasonable Estimates

**MATHEMATICS: Algebra****GRADES 6 - 8**

NM-ALG.6-8.1 Understand Patterns, Relations, and Functions

NM-ALG.6-8.2 Represent and Analyze Mathematical Situations and Structures Using Algebraic Symbols

NM-ALG.6-8.3 Use Mathematical Models to Represent and Understand Quantitative Relationships**GRADES 9 - 12**

NM-ALG.9-12.1 Understand Patterns, Relations, and Functions

NM-ALG.9-12.2 Represent and Analyze Mathematical Situations and Structures Using Algebraic Symbols

NM-ALG.9-12.3 Use Mathematical Models to Represent and Understand Quantitative Relationships

**MATHEMATICS: Measurement****GRADES 3 - 5**

NM-MEA.3-5.1 Understand Measurable Attributes of Objects and the Units, Systems, and Processes of Measurement

NM-MEA.3-5.2 Apply Appropriate Techniques, Tools, and Formulas to Determine Measurements**GRADES 6 - 8**

NM-MEA.6-8.1 Understand Measurable Attributes of Objects and the Units, Systems, and Processes of Measurement

NM-MEA.6-8.2 Apply Appropriate Techniques, Tools, and Formulas to Determine Measurements**GRADES 9 - 12**

NM-MEA.9-12.1 Understand Measurable Attributes of Objects and the Units, Systems, and Processes of Measurement

NM-MEA.9-12.2 Apply Appropriate Techniques, Tools, and Formulas to Determine Measurements

**MATHEMATICS: Problem Solving****GRADES Pre-K - 12**

NM-PROB.PK-12.1 Build New Mathematical Knowledge Through Problem Solving

NM-PROB.PK-12.2 Solve Problems That Arise in Mathematics and in Other Contexts

NM-PROB.PK-12.3 Apply and Adapt a Variety of Appropriate Strategies to Solve Problems

NM-PROB.PK-12.4 Monitor and Reflect on the Process of Mathematical Problem Solving

**MATHEMATICS: Communications****GRADES Pre-K - 12**

NM-COMM.PK-12.1 Organize and Consolidate Their Mathematical Thinking Through Communication

NM-COMM.PK-12.2 Communicate Their Mathematical Thinking Coherently and Clearly to Peers, Teachers, and Others

NM-COMM.PK-12.3 Analyze and Evaluate the Mathematical Thinking and Strategies of Others

NM-COMM.PK-12.4 Use the Language of Mathematics to Express Mathematical Ideas Precisely

**MATHEMATICS: Connections****GRADES Pre-K - 12**

NM-CONN.PK-12.3 Recognize and Apply Mathematics in Contexts Outside of Mathematics

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