W13 Math lesson: Review

Overview

Tip:Review

Review is an important part of learning. It pushes your brain to remember concepts you learned in the past and bring them back to your memory. This helps to make them more memorable in the future.

This semester you started with arithmetic and worked your way up to solving for a variable. This week you don’t have a math lesson, but you do have the opportunity to demonstrate the new skills you’ve acquired. This week there are two exercise quizzes. The quiz is longer this week so it was broken into two parts to make it more manageable.

Math Exercises (Part 1): Covers material from the beginning of the semester up through week 8’s lesson on the least common multiple (LCM) between two numbers.

Math Exercises (Part 2): Covers material starting in week 8 on adding and subtracting fractions with different denominators and continues through the material up through lesson 12.

Since you don’t have a lesson, take advantage of the time you would normally spend on the lesson to work on the review exercises and study any subjects you need. You may take the review as many times as you like before the due date.

Week 13 Math Gathering Activity:

In this gathering activity you will solve a math magic trick using the concepts you learned throughout the course. In the first part of the trick you will apply addition and subtraction. In the portion where you figure out how it works you will apply what you learned about variables, place value, the distributive property of multiplication, and combining like terms.

This is meant to be fun so don’t spend more than 10 minutes on it. You will not be quizzed on any of this.

Read Your Mind Trick

Have the members of your gathering do the following steps.

Pick a whole number between $10$ and $99$ . (Example: $23$ )
Now add the digits of the number together plus $1$ . (Example: If your number was $23$ , add $2 + 3 + 1 = 6$ .)
Next take your original number and subtract this new number. (Example: $23 - 6 = 17$ )
Now look at the following picture and find your number. Remember the symbol next to it. (For example, if your number is $33$ you see a picture of a boat.)

Mind Guessing Game

Tell the students you will now read their mind:
Now I will read your mind….
You are looking at the symbol of a flower in a pot.

How does this work?

If you aren’t looking at a flower in a pot then you made a mistake when doing the math. Here is why.
Look at the digits in your original number and give them the variable names $X$ and $Y$ .
Remember back to the lesson on place value. The digit in the $10$ ’s place says how many tens there are in the number and the digit in the $1$ ’s place is the number of ones. Therefore, we can write a two digit number as $10$ multiplied by the first digit plus the $1$ ’s digit.
So your original number is $10 X + Y$ . (Go ahead and try this to make sure you understand.)
When you add the two digits together plus $1$ you get $X + Y + 1$ .
The original number subtract the new number is then $(10 X + Y) - (X + Y + 1)$

Next use your skills to combine like terms. Remember to use the skill of multiplying the $- 1$ over the parentheses. (Distributive property of multiplication over addition.)

$(10 X + Y) - (X + Y + 1)$

$= 10 X + Y - X - Y - 1$

$= 9 X - 1$

So no matter what you picked as your original number, the new number you should have calculated is $1$ less than $9$ multiplied by the first digit of the number you picked. $(9 X - 1)$

Now look at the image again.

Notice that all the numbers one less than a multiple of $9$ are the symbol of a flower in a pot, so no matter what number you pick, you will always come up with the same symbol.

Conclusion

You may find other examples of “magic” tricks like this as you go through life. They may guess the number you are thinking, or they may guess your age. All of them are based on math.