Minds On
Which one am I?
Examine the following five packages.
Let’s play a guessing game!
The following clues describe one of the packages. Use the clues to guess which package is being described. Record your thoughts using a method of your choice.
After each clue, try to eliminate any packages that don’t match the clue.
Package 1 clues
- This package has a rectangular face.
- It has an even number of faces.
- It has twelve edges.
- It can hold some clothes but not a dresser.
- It can be stacked.
- It has more than one pair of congruent faces that are opposite each other.
Were you able to rule out any of the packages after the first clue?
How many clues did it take before you decided which package to pick?
How did you know you were correct?
Press ‘Answer’ to reveal the correct package.
This set of clues describes Package B.
Using the first clue, we could rule out the sphere (Package A) and the cylinder (Package E) because they don’t have any rectangular faces.
We knew it was Package B after the fourth clue. Before that, we were deciding between Package B and Package C.Let’s try another set of clues.
Which package does the following set of clues describe? Record your thoughts using a method of your choice.
After each clue, try to eliminate any packages that don’t match the clue.
Package 2 clues
- This package has two congruent faces (congruent shapes are exactly the same shape and size).
- It has less than 10 vertices.
- It doesn’t have any edges.
Were you able to cut out any of the packages after the first clue?
How many clues did it take before you decided which package to pick?
How did you know you were correct?
When you are ready, press ‘Answer’ to reveal the correct package.
Press ‘Answer’ to reveal the correct package.
This set of clues describes Package E.
Using the first clue, we could rule out the sphere (Package A) because it doesn’t even have a face.
After the second clue, we could rule out Package B and Package D because both of the rectangular prisms have 12 vertices.
We knew it was Package E after the third clue because an object only has an edge where two faces meet, and faces must be flat. The curved side of a cylinder isn’t flat.
Test Your Skills!
Your turn
Create a riddle for one of the packages.
Try to describe the package using its attributes. Can you include attributes that are congruent?
Action
What is congruency?
Congruent shapes
Shapes are congruent if they have the same size and shape.
Student Tips
Congruent or similar?
To determine whether two figures are congruent, ask yourself if you could perfectly stack one on top of the other. There can’t be any pieces that hang over or are too big. They have to match exactly.
If the answer is “yes,” they are congruent!
If the answer is “no,” we say they are similar.
Congruent shapes activity
Examine the following rectangles, and think about which ones are congruent to Rectangle A. Explain how you know.
Answer the following question.
How did you decide which rectangles were congruent?
Press ‘Explanation’ to reveal the more about these six rectangles.
Rectangle A is congruent to rectangles B, D, and F because they all have the same size and shape. In other words, you could stack these four rectangles on top of each other.
Rectangle A is not congruent to rectangles E and C because they are different sizes. Since they still have the same shape, we say they are similar.
Quick vocabulary review!
Let’s review some key terms.
For each sentence, select the missing word from the drop-down menu.
Are they congruent?
Two students used geoboards to make squares.
The instructions were to make two congruent squares, where each side is 4 units long.
The following are the two squares they created. Student A created the first square, and Student B created the second.
Student A says the squares are congruent because the side lengths are all the same: 1 unit long.
Student B isn’t sure.
Have they created two congruent squares? Explain your thinking.
If they haven’t, what could they do to make the two squares congruent?
Congruent objects
Three-dimensional objects can also be congruent.
Congruent objects have:
- matching edges with the same length
- matching vertices with the same angles
- matching number and shape of faces
One way to tell if three-dimensional objects are congruent is to match them to each other to identify if they are exactly the same. Everything should match perfectly.
Are they congruent?
Student A and Student B were asked to create three-dimensional objects that are congruent.
They placed their objects on a desk.
The front view of each of their objects was a square.
They decided that their shapes were congruent because the front faces were exactly the same shape and size.
Each of their square faces had matching edges with the same length and matching vertices with the same angles.
When the students examined each of their objects more closely, this is what they found:
Side view of Student B’s shape. It is a rectangular prism. It is a solid block and appears to have the same length and width as Student A’s shape.
Are their objects congruent? How do you know?
Consolidation
Searching for congruent objects
Can you identify three-dimensional objects that are congruent to each other in your surroundings?
Find 1 to 3 three-dimensional objects in your surroundings, or from an online platform, that are congruent to the three-dimensional objects we have been learning about, such as a rectangular prism, triangular-based prism, a sphere, or a cylinder.
The following is a student example:
| Three-dimensional object to find | Number of congruent objects found | Name of actual real-life object | Attributes that are congruent |
|---|---|---|---|
|
Rectangular prism |
3 |
Tissue boxes |
parallel side lengths are congruent all angles are congruent |
|
Cylinder |
2 |
Cans |
two end bases (circles) are congruent side length (from one circle to the other) is congruent |
|
Spheres |
2 |
Sports balls |
the height of the two ball is congruent |
Now it’s your turn!
Complete the following fillable and printable Searching for Congruent Objects Chart. You can also complete this activity in your notebook or use another method to record your ideas.
| Three-dimensional object to find | Number of congruent objects found | Name of actual real-life object | Attributes that are congruent |
|---|---|---|---|
Press the ‘Activity’ button to access Searching for Congruent Objects .
Let’s share!
- What were you expecting to find?
- What made it harder or easier to find congruent pairs?
Reflection
How do you feel about what you have learned in this activity? Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.
I feel…
Now, record your ideas about your feelings using a voice recorder, speech-to-text, or writing tool.