Geometer's Sketchpad - Perfect Square Practice

When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do). One of the advantages of doing this is that the bulk of the time spent on the software is actually doing math rather than building something. 

In this sketch students can practice recognizing perfect squares up to 144. It is a very simple sketch not meant to take much time but to just familiarize students with the first 12 perfect squares as well as to remind them that perfect squares can also be defined by physical squares.

• Gr7NS1.6 - represent perfect squares and square roots, using a variety of tools (e.g., geoboards, connecting cubes, grid paper);
• Gr8 - could be used as review or see our square root guesser sketch instead

• All that is needed is the electronic download (below)
• Note that this really works well on an iPad using the Sketchpad Explorer App (which is free)
• You can also use this on any web based computer (or Chromebook) with this Web sketch

This sketch randomly selects a number under 150 and asks students whether it is a perfect square. They can make a mental guess and check their answer. Or, before the check their answer,  if they want to test it out they can try to create a square that has area equal to the given number. Once done they can generate another random number and try again. The hope is that this will help them become familiar with the first 12 perfect squares. Watch this video to see a demonstration of how it works.

• PerfectSquares.gsp (iPad/V5)
• Web sketch here
• For more sketches like this go to my full page

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Christmas Review Activity

This is a Christmas review activity where students will answer exponent, powers of 10, square root and Pythagorean Theorem questions and collect presents on the Smartboard. 

Gr8 Number Sense

• express repeated multiplication using exponential notation
• represent whole numbers in expanded form using powers of ten
• multiply and divide decimal numbers by various powers of ten
• estimate, and verify using a calculator, the positive square roots of whole numbers, and distinguish between whole numbers that have whole-number square roots (i.e., perfect square numbers) and those that do not.

Gr8 Geometry and Spatial Sense

• determine the Pythagorean relationship, through investigation using a variety of tools
• solve problems involving right triangles geometrically, using the Pythagorean relationship

• three (or more) Christmas themed containers (find at a Dollar store)
• exponent, powers of 10, square root & Pythagorean Theorem Questions (copy on cardstock, laminate and cut) 
• solution handout
• Smartboard
• Smart Notebook file with score board
• whiteboard and markers (optional)
• Christmas decorations (optional)
• prizes for winning team (optional)

1. Cut out questions and place some in each of the containers.
2. Spread out containers on a table and add some Christmas decorations (optional).
   
3. Bring up the scoreboard on the Smartboard. (Could create your own scoreboard if a Smartboard is not available)
4. Place students is groups and give each student a whiteboard and marker.
5. Have each group choose a Christmas Tree from the scoreboard.
6. One student from the group will come up and choose a question from a container.  
   
   
7. They will bring it back to their group where all members will answer the question.
8. One person will then come and check their answer with the teacher.
9. The teacher will check off that the group has answered that question.  
10. The student will then drag a present or a Misfit toy under their tree on the Smartboard.  Questions with no candy canes are worth 1 present, questions with 2 candy canes are worth 2 presents and 3 candy canes are worth 3 presents.
11. Collect the question cards as students get them right.  When containers are empty, shuffle the cards and redistribute in containers.
12. The group who collects the most presents and/or Misfit toys will win.  

Note:  There are some special cards that students will find. Each group can have a chance to tap their tree on the Smartboard to play Christmas music.

The video, below, is only visible in the WECDSB domain. That is, only teachers in our school board can see the video if they are logged into their MyTools2Go accounts.

• Exponents, Square root, Pythagorean Theorem Christmas questions (pdf) (doc)
• Exponents,Square root, Pythagorean Theorem Christmas solutions (pdf) (doc)
• Christmas scoreboard (Smart Notebook file) (not)

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Geometer's Sketchpad - Square Root Number Line Guesser

When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do). One of the advantages of doing this is that the bulk of the time spent on the software is actually doing math rather than building something. In this sketch students can practice their knowledge of estimating the square root of numbers up to 500. There are several levels of difficulty: perfect squares up to 100, perfect squares up to 500, square roots up to 100 and square roots up to 500. The intent was that this was built as a practice file for grade 8 students but grade 7 students could use it to practice perfect squares.

• Gr7NS - represent perfect squares and square roots, using a variety of tools
• Gr8NS - estimate, and verify using a calculator, the positive square roots of whole numbers, and distinguish between whole numbers that have whole-number square roots (i.e., perfect square numbers) and those that do not

• All that is needed is the electronic download (below)
• Note that this really works well on an iPad using the Sketchpad Explorer App (which is free)
• You can also use this on any web based computer (or Chromebook) with this Web sketch

Watch the video below to see how the sketch works

• SquareRootNumberlineGuesser.gsp (iPad/V5)
• Web sketch here
• For more sketches like this go to my full page

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Tarsia Puzzle Squares and Square Roots

We came across these puzzles a few years ago. The premise is that you have a bunch of questions and matching answers. Students have cards that have either an answer or question on the edge. They then have to match up the edges that have the pairs of questions and answers and eventually it will make a shape. In this case the activity is matching up perfect squares and square roots.
We found these puzzles originally on the Mr Barton Maths site under the Tarsia Jigsaw Page. The nice thing here is the Tarsia software can be downloaded here (click the green button to download - unfortunately it is Windows only) and you can edit or create your own puzzles. So this puzzle was one of our creations. There are even banks of hundreds of already created puzzles on the site (just scroll down on the Tarsia page and look for the smiley faces for zipped files). These are great puzzles to pull out when you want to break up a long class or have 10 min at the beginning or end of a class to fill.

• Gr7NS - represent perfect squares and square roots, using a variety of tools 
• Gr8NS - estimate, and verify using a calculator, the positive square roots of whole numbers, and distinguish between whole numbers that have whole-number square roots (i.e., perfect square numbers) and those that do not 

Tarsia Card Prep work: There are two downloads (three if you include the actual Tarsia file). The actual cards for the puzzle and the answer card. The cards for the puzzle come on 2-4 sheets (there are different styles of puzzles) and each triangle needs to be cut out (see image tot the right). We have found that if you have several sets of the same puzzle (say if students do it in groups of 3) then it is best to copy each set in a different colour. That way it is harder to get the sets mixed up and easier for clean up after (ie you only need to check if there are 18 cards of each colour). We find that the cards last longer if you laminate them first then cut them.

1. This activity can be done in groups or individually and can take about 5-10 min depending on the student.
2. Hand students the entire set and ask them to match up the numbers written as a square root and its answer.
3. In this case the finished puzzle looks like a diamond.

• Note: this puzzle is a little tricky since all the numbers on the outside edge are not perfect squares and thus have no match. Also there are numbers that appear twice like 16 since it is the root of 256 and has a root of 4

• Square Root Tarsia Cards (pdf)
• Square Root Tarsia Solution (pdf)
• Square Root Tarsia Editable (xjsw)

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks