Fall Problem Solving

The following open-ended assessments require students to apply mathematical concepts and skills to solve problems and explain their thinking using words, pictures and numbers.

• Candy Corn presents a triangular numbers problem using a candy corn pattern. Younger students might use candy corn to model the problem. A sample solution shows how older students might use an input-output table to model the pattern and find the solution without the use of manipulatives.
• Younger students will enjoy analyzing and completing Fall Patterns.  They should then classify the pattern and explain their reasoning as part of the class discussion. It is possible that students will see different patterns in some of the items so their explanation and justification are very important mathematical discourse.
• Annual Fall Parade challenges students to use the triangular pattern to figure out how many students are in the fourth grade. Given the number of full rows, students must apply the pattern and use effective recording (picture, table, etc.) to explain their reasoning.
• See more Problem Solving Resources from the Mathwire collections.  All problems are classroom-ready in PDF format.  Many contain a sample solution for teacher use.
  
  
  
  
  
  
  
  

Spider Math

Be sure to check out Spider Math in the Mathwire Activity Themes.  The spider collection features math mats, name-collection spiders, glyphs and graphing ideas.  Spiders are also the theme of the day for a whole series of games as well as some problem solving activities including insects and spiders problems, which are a twist on the familiar cow and chicken legs and heads problems. 

The games are original Mathwire games designed to develop students' proficiency with important math concepts and skills.  The downloadable PDF files include game mats, directions, recording sheets and game pieces.  The spider games develop coordinate graphing, probability and map coloring, a discrete math topic.

• Catch the Spider Game requires students to roll dice, form an ordered pair, and catch the spider in that square, if possible.
• Spider Game-1 develops the concept of the probability of the outcome of tossing one die.
• Spider Game-2 expands the game to examine the probability of the outcome of tossing two dice and how that change impacts the outcome of the game.
• Spider Web Map Coloring Games require students to use map coloring rules to win the most points in this spider web game.

Teachers may use the Spider Math activities as a Halloween treat or add them to thematic spider units.  The games may be introduced as a whole-class activity, then shifted to the math center for pair play during transition times or indoor recess. 

The Candy Corn Contest

Math-Literature Connection - Estimation:
The Candy Corn Contest by Patricia Reilly Giff

This is a great literature connection for a Candy Corn Estimation Station, as described in the book. The sneaky teacher in this story required that students read a page in a library book for each guess they submitted. Math teachers might vary this requirement to include some fun math practice as a way to earn guessing rights. Either way, incorporating the actual candy corn jar estimation is a great seasonal variation of the Estimation Station described below.


Estimation Station

Establish a regular center in the room which changes weekly. A simple clear plastic container is filled with different items each week. These items should vary in size to challenge students' developing concept of volume, as it relates to smaller or larger units. Use seasonal items: acorns, leaves, candy corn, popcorn kernels, pumpkin seeds, etc. to spark student interest. Keep a class journal of these activities in which students may record their estimates. Record the item and the actual count along with a digital picture, if possible, of the container and the student(s) whose estimates were closest. Some classes involve parents by asking for volunteers to send in appropriate items to be counted. It is important to use the same container for several weeks so that students build an understanding that size matters in estimating how many items there are in the jar.

• Download the Estimation Station Recording Sheet.
• Suggestions for Using the Recording Sheets:  Have students record their names and guesses on page 2.  After counting the actual objects, fill in page 1 and post it in the estimation station.  Circle or color in the student(s) whose estimates were closest to the actual count.
• Take a digital picture of the winner(s) each week and post this picture on page 1, covering the estimation jar clip art.
• Enjoy!!

Symmetric Faces

Halloween masks become a math activity when students create Symmetric Faces.   Each student needs a full sheet of one color construction paper and a half sheet of a contrasting color.  Students fold the full sheet of paper and insert the half sheet inside.  They then free-draw the outline of one side of the face including hair, ear, chin, etc.  After cutting, students open the full sheet and position the half sheet on one side.  They then draw the eyebrows, eyes, nose, and mouth on the half sheet.  Students need to carefully cut out these features and position them on the opposite side to create a symmetric face.

This is a fun holiday project and students learn a lot about symmetry as they correctly position the cut pieces.  It's also fun to see the wealth of ideas students generate from their 1.5 sheets of construction paper.  By varying the paper colors, this activity is appropriate for fall, Halloween, Mardi Gras, Valentine's Day, etc. 

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  Be sure to check out the Mathwire Directions for Creating Symmetric Faces.
  
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  Also visit the Mathwire Symmetric Faces Gallery for some inspiration.  View symmetric faces created by teachers in workshops.
  
  
  

Candy Bingo Cards

Bingo is a great game that provides number recognition practice for pre-kindergarten through first grade students. This set of bingo cards includes 10 different bingo cards and a set of blank cards teachers may use to have students create their own winning cards. The range of numbers they may use for each column is posted at the bottom of each column. This is another terrific skill as students must choose appropriate numbers that fall within each range, including the endpoints in this case.

Download the Candy Bingo Cards for a great seasonal math activity. The cards work for the entire fall season. Teachers may use unit cubes, bingo markers or candy corn for the bingo pieces.   These cards work equally well for family get-togethers with children!

Bat Jamboree

Bat Jamboree by Kathi Appelt introduces the triangular number pattern as bats assemble for the final number beginning with 10 bats in the bottom row, 9 in the next row, etc. to the very top row with 1 bat. Students are introduced to the 55 bats in formation and their various acts but the book "isn't over until the bat lady sings." Students will enjoy this introduction to an important mathematical pattern. Teachers can find many problems that build upon this triangular number pattern and extend the experience.


Student Written Problems: ask students to write original problems that use the triangular number pattern. Being able to write similar problems and solve them require higher-order thinking skills as students apply, synthesize and evaluate both the problems and the solutions.


Check out more Bat Activities in Mathwire's Math Activities Themes collection.

Pascal's Pumpkins

Pascal's Pumpkins encourages students to look for patterns in Pascal's Triangle. The handout develops awareness of this important mathematical pattern through this timely seasonal activity. Students who take higher math courses will meet Pascal again in many different applications, including probability. This handout is an outgrowth of the Rutgers Universiy Discrete Math Institute.

Download Pascal's Pumpkins.  The PDF file contains the student handout and a detailed explanation of the different patterns students might find.  Be sure to make an overhead copy of the pattern so that students are easily able to point out patterns and explain the pattern that they see as they fill in the empty pumpkins.

Extend the activity by asking students to draw and label the numbers in the 7th, 8th, etc. row.  How does identifying the patterns help them complete this task more easily?

Mad Monster

Add this coordinate graphing activity to your Halloween collection.  Students will practice identifying coordinate pairs as they color in the grid to create this picture.

View and download the Mad Monster coordinate graphing activity.  The PDF file contains the grid, key and completed picture.

Grab the Candy Corn Game

This game was designed to provide practice in coordinate pairs. Students place candy corn on the game board, then toss two dice to make an ordered pair. The player removes a candy if there is one on the space and then the other player takes a turn. Teachers may use real candy corn or the candy corn game pieces provided with the gameboard.

View and download the Halloween/Thanksgiving version of the Grab the Candy Corn Game. This PDF document includes the game board, optional game pieces, directions and a recording sheet.

Also check out the Grab the Candy:  M and M Version for an additional resource to use with students during the holiday season.  The PDF document includes the game board, optional game pieces, directions and a recording sheet.

Jack-O-Lantern Coordinate Graphing

It's fun to include seasonal activities during the fall and Halloween season.  Here's a great graphing experience to add to your fall collection!

This activity requires students to use the grid code and crayons or markers to create a jack-o-lantern on a blank 9x9 grid. The use of letters on the horizontal axis and numbers on the vertical axis introduces young students to coordinate pairs without the confusion of the standard (h,v) format. Notice that it is important that elementary students become accustomed to listing the horizontal coordinate first as this will transfer to the Cartesian coordinates they will use in later grades.

View and download the Mathwire Jack-O-Lantern coordinate graphing activity.

Be sure to check out all of the Fall Activities in the Mathwire Seasonal Math Activities collection.

Pumpkin Math

Check out the newest addition to Mathwire's Math Activity Themes collection: Pumpkin Math. This collection capitalizes on students' natural preoccupation with all things pumpkin during the fall and Halloween season. Activities and resources include math mats, measurement, symmetry, games, math-literature connections, glyphs & graphing ideas, problem solving and links to additional internet activities.

Check out Pumpkin Math.