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MATH LESSONS

NUMBER SENSE & NUMERATION MEASUREMENT GEOMETRY
  "Bigfoot Lives!" "The City of Angles"
 
PATTERNING & ALGEBRA DATA MANAGEMENT PROBLEM SOLVING
"Two of Everything" "Survey Says..."
"4Ts Consumer Report"
"Grade 4 Takes a Survey"
"Problem of the Day"
"Problem Solving on the Internet"
     

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The City of Angles (Topic - Geometry)

Challenge your students to plan and draw a geometric city which demonstrates their knowledge of angles and shapes. Following your background teaching of types of angles and shapes, have students design The City of Angles. The only rule... the city may only include angles, straight lines and geometric shapes. Expand this idea with a language focus by having students generate lists of possible names for the components of their city (eg Pentagon Park, Tri-Mart Mall, etc.) As a further challenge, have your students find the perimeter or area of certain sections of the city. Students could also try drawing their city to scale.

Idea adapted from Instructor Magazine
- Shayni Tokarczyk

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Two of Everything! (Topic: Functions)

This is a great idea to accompany your resources collected from Peter’s recent workshop on Patterns and Functions. Begin by telling students that you have recently read a story about a magic pot that changes numbers in a special way (Don’t tell them that the pot doubles whatever goes in). Draw a chart with two columns, one labelled IN and the other OUT. Challenge students to figure out what is magic about the pot as you begin to fill in the chart. As students suggest numbers and write them in the IN column, you fill in the number that would match it in the OUT column. (e.g. when 10 goes in, 20 comes out). Record several numbers until students begin to catch on to the pattern. Discuss. "It doubles" will likely be the common answer. At this point, relate the term "function" to the predictable pattern they have discovered. Now, read "Two of Everything" by Lily Toy Hong (1993), a Chinese folktale about a couple that dig up a large, old brass pot and discover that it is magic (it also doubles everything that is put into it!) This literature link is perfect for reinforcing your earlier story. Challenge students to think of functions for their own magic pot. Using charts, students create their own patterns and work with a partner to discover each other’s functions. Now hold a discussion to determine what makes a function easy or hard to guess.

- Shayni Tokarczyk

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Problem of the Day!!!
Challenge your students with a "Problem of the Day!"
Here are examples from each strand!

Number Sense
The Chen family has four children. The sum of the children’s ages is 17. The product of their ages is 250. All children are younger than seven including the triplets, who are older than their sibling. How old is each child?
Answer: Their ages are 2, 5, 5, and 5

Probability (Use one set of tangrams)
All 7 tangrams are in a bag. Without looking, you reach in and pull out one tangram. What is the probability you will have: (1) any triangle, (2) a small triangle, (3) a large triangle, (4) a quadrilateral, (5) a circle?
Answer: five sevenths, two sevenths, two sevenths, two sevenths, zero sevenths

Patterns (Use a calculator)
Find the next three numbers in the series. What is the pattern? 5 10 40 240 __ __ __
Answer: 1920; 19 200; 230 400 - (x2), (x4), (x6), (x8), (x10), (x12)

Measurement (Use a calculator)
Lucky Luke just won a tenth of a million dollars in a math contest! The only way he can keep the money is if he can figure out how many days it would take to give it away at the rate of 50 a second. Help Luke to figure it out, and he says he’ll give you half. He has three minutes to find the answer. GO!!
Answer: 2.3 days

Geometry
Sunny’s Dad just baked her a chocolate layer cake for her birthday. She is having five friends over to eat it. Four of those friends really don’t like chocolate cake, but they’ll eat a small piece. One of Sunny’s friends likes chocolate cake as much as she does. Draw a circle. Now draw three straight lines so that Sunny and her friends will get the proper pieces.

Source: Daily Problems and Weekly Puzzlers (Grade 4) by Brad Nitschneider

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Problem Solving on the Internet
Visit these sites to collect more super problem solving resources...

arrow.gif (5402 bytes) Digital Education Network Great math puzzles to work on!
arrow.gif (5402 bytes) The Math Forum

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The Survey Says...

One of the activities that my Grade 4/5’s loved to do independently was a school-wide survey. Our regular Spirit Days offered the perfect opportunity for the students to conduct their survey. I assigned a group of three to tour the school with their clip boards (they feel very professional!) and to complete our "Survey Says..." tally sheet (See NAJE News Volume 1 Issue 2). The group is then responsible for the calculation of all results and they present their findings to their classmates and sometimes to the school through the PA system (very motivating!). Students simply fill in the blank(s) for what they are surveying (example: Number of students who participated by wearing red on Valentine’s Day), record how many students were (1) present at school in each class that day and (2) how many students participated. They then return to class and work together to tabulate the results. They find the percent using the formula and record their calculations. Finally, I have them complete a group evaluation. Using guidelines which we had previously discussed for completing group evaluations, they fill in the box to report on how they did. This form can be used in a variety of ways and will work in many different subject areas. To take this further, students could graph their findings, analyse trends and try to devise ways to encourage greater participation in the school. You can see the range of possibilities such as an art lesson to create posters to advertise upcoming Spirit Days, etc. Have fun! It is a great way to make your students feel really important!

- Shayni Tokarczyk

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4Ts Consumer Report

I use this activity with my Grade 4s as it meets several of the specific expectations for data management and the kids love it because it is "real math"!

Materials: Materials: a Consumers Report Buying Guide
                   photocopies of individual graphs (be sure to site source) and questions

Specific Expectations:
1) identify examples of the use of data in the world around them
2) recognize the purposes of different parts of a graph
3) read and interpret data presented on tables, charts, and graphs and discuss the important features

Every year consumers can purchase a Consumer Reports Buying Guide that provides purchasing data for a variety of products (eg computers, cars, bicycles, VCRs, TVs). This book (which can be purchased for under $10) contains a wealth of graphs that can be used effectively in your program. My students created their personal 4Ts Consumer Report book after we discussed what the book was all about and looked at several examples of the contents. Each day for a 2 week period, I gave the students a page consisting of a graph from the Report and several questions for them to answer. The questions required them to interpret the data and do some higher order thinking. So some questions were standard "read the graph" type questions but some really challenged the students and gave them a chance to do some "real life" problem solving. For example, when I gave them the data for VCR repairs I asked questions such as "If your job was to fix VCRs, which one would you want people to buy? Why?". I also threw in some numeration questions where students had to complete calculations and report their findings. Some questions ("If you were a VCR salesperson, which brand of VCR would you want to sell in your store? Why?) resulted in interesting conversations regarding ethics! After the 2 week period the students had completed several analyses of various types of graphs. I then had them use the computer to write their own report for Canadian consumers about the various products. The students did a super job and were able to "back up" their reports based on research!

- Shayni Tokarczyk

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Grade 4 Takes A Survey

In Volume 1, Issue 2 (NAJE Newsletter), we featured "The Survey Says..." by Shayni . This issue we revisit that form. The Ontario Curriculum Grades 1-8 Mathematics states that "the focus should be on real-world questions. ... Students should talk about their ideas and use the results of their experiments to model situations or predict events. The topic of probability is rich in interesting problems that can fascinate students and provide bridges to other topics such as ratios, fractions, percent and decimals." We believe that this form is one tool that will allow children to explore real-world events happening in their school environment. Here is an example of how it has been used in my classroom this year. Lots of math happened with this survey and all graphs were made on the computer. A copy of the original survey form can be found in Volume 1, Issue 2 or by contacting Shayni or myself. If you use this format or something similar, please send us your results so that we could share in a later issue.

Grade 4 Takes a Survey
Who owns a cat, a dog or both a cat and dog?


After the girls collected the data, the students answered these questions:
1. How many children took the survey?
2. How many children have just dogs? just cats? both?
3. Do the children have more dogs or cats?
What is the difference?
4. Find the fraction and per cent of students who: (check your survey sheet for formula)
Have dogs?
Have cats?
Have both?
5. How many Junior students were there who took the survey?
How many own dogs?
Own cats?
Own both?
Find the fraction and per cent of each and record above with your answers.
6. How many Primary students were there who took the survey?
How many own dogs?
Own cats?
Own both?
Find the fraction and per cent of each and record above with your answers.
7. Make a bar, line or pictograph graph for one of the categories.
8. What did you learn?

- Linda Miller, Grade 4, South, 1998

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Bigfoot Lives!

Teaching your kids how to estimate the area of objects? This is a really fun activity that the students love doing. After teaching your class how to estimate the area of objects, provide them with a legal-sized sheet of paper with a large squared centimeter grid. Have them trace their bare foot onto the centimeter paper (a partner helps here). Students record full squares, "almost" full squares and half squares. They add these up to find the estimated area of their foot in squared cm. To make this activity really fun, use chart paper and have the kids record their name, their estimate of the area of their foot, their actual measurement and their guess of which student will have the biggest foot. The kids love guessing who will be the class "bigfoot". I usually have each pair of students swap papers and check the areas before they record their actual measurement. When it is all over we create a bulletin board with our chart, the kids papers, giant footprints and a picture of Bigfoot himself with the face missing. We put a picture of our classroom bigfoot's face right on the one of Bigfoot. It is a riot and the kids learn a lot too!

- Shayni Tokarczyk

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Last Updated on December 21, 2014