Rotation

This week we learned the topic of rotating shapes. We learned that

• Rotation won't change a shape
• When there are multiple parts in a shape, rotation won't change their order (relative position to each other -- thinking about left/right neighbors)

Homework

Lydia draws a flower with 5 petals. She wants to color the flower using red and green. How many different flowers can she draw with these two colors? Note that some flowers may appear to be different, but they are actually the same (because they overlap each other after proper rotation). Example below:

A) 6          B) 7             C) 8                D) 9                   E) 10

Read the following hint if you get stuck.

Hint: this question is a little harder than those we looked at during the class. A good strategy is to solve the problem in two steps: first step is to find out all the color combinations. For example, one color combination is one red petal and four green petals; and another combination is two red petals and 3 green petals; and so on. Once you've done that, the second step is for each color combination, find out how many different flowers you can make. After you figure that out, you can get the answer by adding the flowers from all color combinations.

Folding and Symmetry

Today we continue learning about symmetry. Especially we learned how to solve folding problems. In order to find out the shape after folding and cutting, one common strategy is to draw the image as you unfold it using the mirror image method.

Homework

1. A square is folded 3 times into a triangle as shown below. Before folding and cutting using paper and sissor, try to draw how image look like when unfolding using the mirror image method.

2. This problem is an example of a classic folding puzzle. Take a piece of blank paper.  Divide it into 8 sections and label each section with a number from 1 to 8, as shown below. Fold this paper along the lines so that the numbers lie on top of each other in order from 1 to 8.

Topic. Symmetry

Today we learned about symmetry and mirror image.

• Symmetric shape can be folded along the line of symmetry, so that one half matches the other
• Mirror images are opposite. 
• For example, when you look at yourself in the mirror, left and right are reversed.

Homework
1. How many lines of symmetry does this snowflake has?

2. Tom has a clock on his bedroom wall. There is a mirror on the opposite side wall. The clock only has the ticks to mark the hours. It does not have the numbers (like the one below). One day, Tom looks into the mirror and reads the time from it; then he turns around and reads the clock directly, and he finds the time is the same. What time is it when Tom reads the clock?

Topic: Finding Orders

Today we learned about orders, and how to find then from clues. The strategies we used include:

• Draw a line, and label the positions 1, 2, 3, 4, ..., and then:
• put person's name at the position if you know it, 
• and you can also determine if the person should be put to the left or right depending on in the information given in the problem
• Also, we can use 'exclusion' method. For example, when the question asks for who is the oldest person, you can start by excluding the person that is not the oldest. If there is only one person left at the end, that is the answer.

Homework

1. Basil attached five stickers with the digits 1, 2, 3, 4, 5 in some order on a sheet of paper as shown in the picture.

In what order could Basil have put the stickers? 1-2, 5pt

(A) 1, 2, 3, 4, 5 (B) 4, 5, 2, 1, 3 (C) 5, 4, 3, 2, 1 (D) 2, 3, 4, 1, 5 (E) 4, 1, 3, 2, 5

2. Anne, Clara, Michael and Dan had an apple eating contest. Dan ate more apples than Clara, and Michael ate fewer apples than Anne. We also know that Dan did not win the contest. Who ate the most apples?

A) Anne        B) Clara   C) Michael     D) We cannot know.