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Goals
• Play with some math apps• Find ways to enrich student learning
while using these apps• Learn and possibly explore apps that
are new to you and make you excited about teaching math.
There are two choices for levels. Within each game there are levels and changes in difficulty as you proceed through the game.
In the 9-bubble game, the object is to choose numbers so that the sum of any three of them is equal to the specified sum.
In the 16-bubble game, the object is to choose numbers so that the sum of any four of them is equal to the specified sum.
Deep Sea Duelhttps://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Deep-Sea-Duel/
Before we start using technology let’s do a quick experiment.
Find different ways to make 15 using the numbers 1 to 9 using the following rule:
You must use 3 different numbers. How many choices do you think there are? Put your estimate in the chat box.
Now put in the chat box some choices and let’s see if we cangenerate all of them.
I will record as many as I can.
1 + 7 + 7
1 + 6 + 8
1 + 5 + 9
1 + 4 … ugh!!! 1 + 8 + 6
1 + 9 + 5
2 + 3 +… 2 + 4 + 9
2 + 5 + 8 2 + 6 + 73 + 4 + 83 + 5 + 7
3 + 6 + 63 + 7 + 5
4 + 2 + 9
4 + 3 + 8
5 + 1 + 9
5 + 2 + 8
5 + 3 + 7
5 + 4 + 6
1 + 7 + 7
1 + 6 + 8
1 + 5 + 9
1 + 4 … ugh!!! 1 + 8 + 6
1 + 9 + 5
2 + 3 +… 2 + 4 + 9
2 + 5 + 8 2 + 6 + 73 + 4 + 83 + 5 + 7
3 + 6 + 63 + 7 + 5
4 + 2 + 9
4 + 3 + 8
5 + 1 + 9
5 + 4 + 6
1 + 7 + 7
1 + 6 + 8
1 + 5 + 9
1 + 4 … ugh!!!
1 + 8 + 6
1 + 9 + 5
2 + 3 +…
2 + 4 + 9
2 + 5 + 8
2 + 6 + 7
3 + 4 + 8
3 + 5 + 7
3 + 6 + 6
3 + 7 + 54 + 2 + 9
4 + 3 + 8 5 + 1 + 9
5 + 4 + 6
Now let’s play Deep Sea Duel !!!
Also what number did we use the most? Does it remind you of another game?
Once the numbers change from 15 to a different sum. Look out the pattern with the numbers selected compared to the number 15. How do you use what you learned from playing the sum of 15? What pattern do you notice?
4 + 2 + 99 + 5 + 19
3, 5, 7, 9, 11, 13, 15, 17, 19 1 , 2, 3, 4, 5, 6, 7, 8, 9
3 compared to 15 compared to 2
7 compared to 3
2 larger, 3 larger, 4 larger
5 + 3 + 10
4X2 +1
1 , 2, 3, 4, 5, 6, 7, 8, 98, 11, 14, 17, 20, 23, 26, 29, 32
5, 6, 420, 23, 17
4x5 - 3
6, 8, 10, 12, 14, 16, 18, 20, 22 1 , 2, 3, 4, 5, 6, 7, 8, 9
4 + 2 + 912 + 8. + 22
2X9 + 4
1 , 2, 3, 4, 5, 6, 7, 8, 9
4 + 2 + 9
6, 9, 12, 15, 18, 21, 24, 27, 30
15 + 9 + 30
3x4 + 3 3x2 + 3
Pan Balance Shapes - NCTM Illuminationshttps://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Pan-Balance----Shapes/
1. Put only on the left side only. You can not change the left side and balance on the right side.
Write the sentences that go with the results.Ex: 3B = 6R3B = 4R + 2 Y3B = 3R + 1PQuestion: Do you notice anything from your results.
2. Try different combinations on the left side, write all the possibilities.3. Test out the other sets and see what happens.
Directions of algebraic thinking in using the pan balance shape
Pan-Balance Numbershttps://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Pan-Balance----Numbers/
Some suggestions:1.Put a number such as 600 in the red (left) pan. Now balance the blue side using at least 3 different operations without using 1 as a multiplier or 1 as an addend. You must do at least 5 different combinations. (You can not change the red side)2.Extensions: you must use at least divisionand Parentheses.
Fractalshttps://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Fractal-Tool/
You can use this as part of learning patterns and fractions. Students can make their own. Example below, shows that if you start with a large orange block and break it into 4 parts with 3 are orange blocks and 1 white. Each step the orange block breaks down into 4 smaller pieces.
This tool does not work on chrome!!!!!
Equivalent Fractions only works on Firefox or Safari…. Try it on your own but it does not work on chrome!!!!https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Equivalent-Fractions/
https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Fraction-Models/
https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Fraction-Game/
https://apps.mathlearningcenter.org/number-line/
Math Learning Center Appshttps://www.mathlearningcenter.org/resources/apps
https://apps.mathlearningcenter.org/number-pieces/?3k8a78t3
https://apps.mathlearningcenter.org/number-line/?3rqsx24k
3RQS-X24Khttps://apps.mathlearningcenter.org/math-clock/?kbqbek2w
KBQB-EK2W
3K8A-78T3
Try these already made
https://www.mathlearningcenter.org/resources/apps/fractions
Great source for comparing, adding, subtracting fractions
Geoboards: https://www.mathlearningcenter.org/resources/apps/geoboard
Playing jump on the geoboard.
Rules are that you are given a number and you have to jump thatNumber of pegs. If you are given the number 2, then you startfrom the top and jump 2 pegs and connect. Keep going until you Get back to the start.
I would like you to try. Let’s do the following
Take the letter of your first name and add 2. Use this as your jumping number. Exceptions of course is that if you are over 16, then divide your number in half and if odd, Use either below or above it.
Next challenge is to do 2 jumps. You pick any pair of numbers that you want. Size of number does not matter. Why does the sizeNot matter?
This is the beginning of3, 5. How many times willtake to get back home?
https://tinyurl.com/yydtnbhzFlippity for making your own games: https://flippity.net/
Adapted from https://www.youcubed.org/
1. Start with a list of numbers (ex: 2,5,4,7,1)
2. Using the following pattern for directions:Right, down, left, up
3. Spiral through list.
4. Repeat the spiral until either you Return back to start or just see pattern.
Spiralaterals
This example is one spiral and continue withStarted: 2 right 5 down 4 left 7 up 1 right 2 down, 5 left, 4 up, 7 right, 1 down2 left, 5 up, 4 right, 7 down, 1 left2 up, 5 right, 4 down, 7 left, 1 upStart over again,
2, 1, 2, 1, 2, 1, right
2, 1, 2, 1, 2, 1, left
3, 2, 1, 3, 2, 1, right
3, 2, 1, 3, 2, 1, left
3, 2, 2, 3, 2, 2 right
3, 2, 2, 3, 2, 2 left
3, 1, 1, 3, 1, 1, right3, 1, 1,3, 1, 1, left3, 2, 1, 3, 2, 2 left
3, 1, 1,1,1, 3 right
3, 1, 1,1,1, 3 left
1,1, 2, 2, 3, 4 right
1,1, 2, 2, 3, 4 left
https://apps.mathlearningcenter.org/geoboard/Try these below and see what happens.
Bobbie Bearhttps://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Bobbie-Bear/Finding combinations. Introduce the meaning of multiplication to find the choices.
• https://mathforlove.com/2020/03/diffy-squares/
• https://nrich.maths.org/12162
More Sources:
Diffy Squares
https://mathforlove.com/2020/03/diffy-squares/
https://www.potentialplusuk.org/wp-content/uploads/2017/06/Potential-Plus-UK-Challenge-13.pdf
10
7
34
21
24
3 13
14
Find the differenceBetween 10 and 7
Find the difference between 10 and 34
Find the differenceBetween 34 and 21
Find the difference between 7 and 21
Coding as part of Mathematics.
https://scratch.mit.edu/projects/301453330/
https://scratch.mit.edu/projects/301453624/
A sample of what could be done in scratch from MIT
Here are some projects to try in scratch which are similar to the activities in other slides
More info on Math Learning Center Appshttps://www.mathlearningcenter.org/resources/apps
https://www.mathlearningcenter.org/resources/apps/math-clock
https://apps.mathlearningcenter.org/geoboard/
https://apps.mathlearningcenter.org/number-rack/
https://apps.mathlearningcenter.org/number-frames/
https://apps.mathlearningcenter.org/partial-product-finder/You can break up the array into any size pieces.
https://apps.mathlearningcenter.org/fractions/
Link to even more manipulativesLink to a listing of other manipulatives from other sources. (from BAMS- Boston Area Math Supervisor)
Cuisenaire. Rods: https://nrich.maths.org/4348This is part of the nrich website which has many activities.
Nrich has many resources but my favorite is Cuisenaire Rods
Thank you for coming. Susan Weiss, [email protected]
Link for presentation also.
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