Using Virtual Manipulatives to Solve Problems & to Explore


Number - Patterns & Relations - Space & Shape - Statistics & Probability


Additional Resources: SK outcome based lessons & assessment of problems using concrete manipulatives & virtual manipulatives.

Grade

Number

Problem

Manipulative

K
NK.3
Ask students to build two towers, 1 purple, 1 Yellow. Count and record the number of cubes in each tower.
Connecting Cubes

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1
N1.1
There are 10 bears and 2 boats, how many bears will sit in each boat?
Teddy Bears
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1-2
N1.1 & N2.1
Show me 2 ways to make 20

Show me 2 ways to make 59
Tens & Ones
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1
N1.1
Pick a number. Write it down. Show the number using pictures. Write down the number that comes after it.
Draw.to

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1
Addition
N1.9
Read the Story 10 Little Monkey's (pause anywhere in the story) ask students:
If some jumped off, how many are left on the bed?
A. Draw your answer
B. Write a number sentence
C. Share your answer
10 Little Monkeys - Virtual Story
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Draw.to
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1
Addition
N1.9
You have 10 Teddy Bears, some are blue and some are yellow. How many combination's can you make to show 10? Explain or draw the different combination's. Use pictures, numbers or words.
Select Bedroom background, & Teddy Bear Manipulative
Teddy Bears
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1
Subtraction
N1.9
Follow the egg carton problem
Fill the Egg Carton
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1
N1.9
Changing Rods Stories to Number Sentences


Mystery Train Clue Cards: Original Lesson


Gordloina
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Cuisenaire Rods
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2
N2.1
What's My Name: I'm Greater than 10, I'm an even number, I'm less than 25 ... show using this 100's square

Bob has a number between one and one hundred. His number has a four in it. What could his number be?
100's Square
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2
N2.2
Relationship between Addition and Subtraction
Number Bars
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Counting Fish
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Thinking Blocks
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Ten Frames
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3
N3.1
I am 3 digit number, my digits are 3,8,1, how may different numbers can I make?
Base Ten Blocks
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3
N3.1
I have 6 coins worth $.82. What coins do I have? Is there more than 1 answer?
Mark has 4 coins, how much money does he have? Are there other answers?
I have some pennies, nickels and dimes in my pocket, I put 3 coins in my hand
Money Matters (Link Broken)

3
N3.1
How many ways can you use the calculator at add 4 fives?
Big Calculator
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2-3
N3.1 & SP3.1
There are 20 students in the classroom, most of the students took a bus, the least amount of students drove in a car ... show your work (using tallies)
Tally
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Mrs. J. spins the spinner - the arrow is more likely/least likely to land on?? (change the spinner)
Virtual Spinner
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3
(N3.4)
Let students explore halves & quarters
Fraction Flag
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4
N4.6
Show me a flag that is painted 8/16 red, 5/16 Blue and 3/16 yellow
Create your own Flag and explain in fractions how it is painted
Fraction Flag
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4
N4.1 & N4.2
Choose a number from the random number generator. Represent the number in two or more ways.
Random Number GeneratorPicture_25.png
4
N4.8a
We want to buy some rope. One rope needs to be 2.47 metres in length and the other
rope must be 1.78 metres in length. How much rope altogether must be purchased?
(Source: Mike Fulton & Instructional Video)
Base Ten Blocks
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5
N5.4
Calculate how old you are in months/weeks/days. (Guess & Check Strategy) Estimating
Calculating Tool
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5
N5.5
Gina and her friends ordered the same size pizza but had it cut twice as many times as Jason and his friends. How many pieces of pizza would Gina have to eat to equal the amount Jason ate?
How many pieces of pizza would Gina have to eat to equal the amount Jason ate?
Source: Mike Fulton - Instructional Video
Fraction Pieces
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6
N6.2
Arrange the four number cards (1, 2, 3 and 21) on the grid above to make a diagonal, vertical or horizontal line. You can put a number card on a square with
  • the same number
  • a multiple of that number
  • a factor of that number.

In how many different ways can you do it?
Factor Lines
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6

Show how many ways you can change from a $20.00 bill if the item you purchased was $14.56?
Money Matters (broken-link)

7
N7.3
Students will answer questions to guide them to find patterns between decimals and the equivalent fraction.


7
N7.6
Number line

7
N7.6
2 Coin problem about the weather

Grade

Pattern & Relations

Problem

Manipulative

1
P1.2
If I had a (aabcaabc) pattern, how would this look with pattern blocks?
Could use Kidspiration: Example
or the virtual manipulative
Pattern Blocks
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1
P1.2
Follow the Pattern
Pictorial Symbols & Patterns
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2
P2.3
Ask students questions ... if you have 8 on this side and 4 on the other side how many more would you need to (=) 8
Getting the Balance
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3-4

Jane has the number 93 on her calculator, presses some buttons to get
88,83,78. What rule matches the number pattern .ie (add 5)
Calculator & 100 Chart
Picture_31.png
4
P4.1
Count by 8's and let students visualize and verbalize the pattern - Discuss
Hundred's Chart
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4
P4.1
Start at 5, count on 6 more, what is the number? Count on 2 more, what is the number? Count on 10 more, what is the number? Count on 4 more, what is the number? Repeat this 15 and 25 .. what do you notice?
Hundred's Square
Picture_14.png
7
P7.1
It's a hot summer day, and Eric the Sheep is at the end of a line of sheep waiting to be shorn. There are 50 sheep in front of him. Being an impatient sort of sheep, though, every time the shearer takes a sheep from the front of the line to be shorn, Eric sneaks up two places in line.
Eric the Sheep
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7
P7.3

Task: Kerri is a contestant in a school spell-a-thon. A contestant receives 3 points for every word spelled correctly. Because of a technical penalty, Kerri loses 5 points. She now has 19 points. How many words has Kerri spelled correctly? Model the problem with algebra tiles and then use the tiles to solve the problem. How can you use the algebra tiles to verify your solution?
(Source: Mike Fulton - Instructional Video)

Alge-Tiles
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7
P7.4

Problems x + 3 = 7 r + 5 = -2 3x – 4 = 5
(Source: Mike Fulton - Instructional Video)
Algebra Tiles
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8
P8.1
"Today we are going to experiment with the Tables and Chairs applet and see if we can identify any patterns. We will try to describe any patterns we find both and mathematically. "* answer the question "How do you describe a pattern mathematically?"
  • answer the question "What is an ?"
  • discuss finding patterns in numbers.
Table & Chairs
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Grade

Space & Shape

Problem

Manipulative

1
SS1.1
Capacity Target Container

1
SS1.3
Can you complete the square?
Square

Picture_36.png

2
SS2.1

Non-Standard Measurement
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3
3D Objects
SS2.3
With a partner look Describe the following shapes - cubes, spheres, cones, cylinder, pyramids
3-D Shapes
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3
2D Objects
SS3.5
Sort the Blocks: Decide on a 'rule', such as four-sided shapes or large shapes
Sorting Logic Blocks

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4
SS4.4
Find 2 polygons other than a square and rectangle whose reflections are identical to the original. Show using the geoboard
Virtual Geoboard
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5
SS5.1
Sally's Yard- This problem allows the students different ways to solve a real-life perimeter problem.
Click on this Smart File to view the problem
5
SS5.3
Use the white rod to introduce the concept of volume. Identify the volume of the white rod as 1 cubic unit. Have the students build figures of their own choosing or following a specific pattern you provide. Have them find the volume of each figure by determining the number of cubic units it holds.
Cuisenaire Rods

Picture_13.png

6
SS6.2
Identify the face of one of the white cubes as 1 square unit. Have students build figures using a variety of rods. Have students determine the surface area of the figure as well as its volume.
Cuisenaire Rods
Picture_13.png
6
SS6.2

Things to explore: 1. How many rectangles can you make with a perimeter of 16 units? What is the area of each?
2. What happens to the area of a rectangle as you increase the perimeter?
Problem: Tina’s puppy has a pen that measures 2 m by 3 m. Because her puppy has grown so much, her dad plans to double the length and width of the pen. What will happen to the area of the pen after her dad makes these changes?
Another problem: A and B are two flat rectangular fields. The fence around field A is longer than the fence around field B. Does that mean that field A has a greater area than field B? Explain and use a model or sketch to support your solution.
(Source: Mike Fulton - Instructional Video)
Area & Perimeter Tool
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Virtual GeoBoard
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GeoBoard
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7
SS7.2
Make the following figures:
A square with an area of 4 square units
An isosceles triangle with an area of 4 square units
A square with an area of 2 square units (this is not a question!)
Exploring Area with a Geoboard

Picture_42.png
Virtual Geoboard
Picture_40.png
8
SS8.1


What is the distance from home plate to in baseball?
The distance between the bases from 1st to 2nd to 3rd to home is 90 feet.

What length of a ladder is needed to reach a 5 m high rooftop if the ladder is places 15. m from the wall of the house?

Source: Mike Fulton - Instructional Video
Pythagoream Theorem Applets
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The Proof
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Pythagoream Theroem & Baseball
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8
SS8.3
Picture_4.png

8
SS8.4
Design a tessellating pattern
Each time you tessellate the pattern, review which polygon you started with, what types of symmetry are present in the finished tessellation, and experiment with a variety of colors to see the different effects
Tessellate
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Tessellation
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Grade

Stats & Probability

Manipulative

7
SP7.3
The sections are equal and the spinners are fair. If each spinner is spun once, what is the probability that the sum of the numbers on the spinners is 6?
Dice & Spinner
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7
SP7.3
Examining the relationship between Theoretical Probability and Experimental Probability through the game of 'Rock, Paper, Scissors'.

Paper, Rock, Scissors - play against the computer
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8
SP8.2
2 dice are rolled. What are the chances that one will show a number less than 4 or a number greater or equal to 5? Independent Events with 2 dice Example
Dice & Spinner
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