Math 180 Block 6

Modeling/Make a Rule

100

Using 16 blocks, make an array representing 4/9 of 18

(x) will represent a grouping in a block. X will represent a block. 9 rows of 2 in each column. Four groups are circled out of the 9. (X X ) (X X ) (X X) (X X) X X X X X X X X X X

200

Using 20 blocks, model 3/5 of 20

(X) represents a group; X represents a block. 5 groups of 4 in a row with 3 groups circled to represent 3/5 0f 20. (XXXX) (XXXX) (XXXX) XXXX XXXX

300

Using Models to divide represent the problem using Fraction Shapes. 2 Divided by 2/3 (You will begin with 2 circles that will need to be divided)

The two circles will break into three sections/pieces. I will break out pieces, 2 at a time, into three sections. So when I divide 2 by 2/3, I will get 3 for an answer.

400

Find the rule Input Output 1 1/4 2 1/2 3 3/4

What is Multiply by 1/4

500

Identify the Rule using the information below: Input Output 1/2 7/2 1/5 7/5 2 14

What is Multiply by 7

Make an Estimate

100

Estimate 1/2 of 1/8 (Is your estimate less than, greater than, equal to 1/8 ?)

Answer will be LESS Than (<) 1/8 Why? Because taking 1/2 of 1/8 is smaller than 1/8. When you multiply 1/2 x 1/8 you will get 1/16 which is also smaller than 1/8.

200

Estimate 1/5 of 1/10 (Is the answer Less than, Greater Than or equal to 1/10)

Answer would be < Less than 1/10. If I am taking 1/5 of 1/10 then my answer is a part of 1/10, smaller piece. If I multiply 1/5 x 1/10, I will get 1/50 which is smaller than 1/10.

300

Estimate 3/2 x 5/9 (Is it greater than, less than, or equal to 5/9 ?)

It is GREATER THAN 5/9 because you are multiplying by a number greater than one ! (3/2) is more than one. If I really multiplied, my answer would be 15/18, which is almost 1 and bigger than 5/9 !

400

Estimate 7/10 x 3/10 (Is it greater than, Less Than or equal to 3/10)

It is LESS THAN 3/10. Both fractions are less than one and I am taking a fraction of the other fraction, making it smaller. 7/10 x 3/10 would equal 21/100 which is smaller than 3/10.

500

Estimate 3/4 x 4/3 Is the answer Greater Than, Less Than or equal to 3/4 ?

Answer is GREATER THAN 3/4. One number is Larger than 1, which makes the answer bigger when multiplying. 3/4 x 4/3 = 12/12 12/12 is greater than 3/4.

Problem Solving

100

Curiosity, a mars rover, is 10 feet long. The length of Sojourner, another rover, is 1/5 the length of Curiosity. How many feet longer is Curiosity than Sojourner ?

Using a model, you would have 10 feet represented with 5 blocks for Curiosity. Sojourner would be one block, since it is 1/5 the length of Curiosity. You will see that taking 1/5 of 10 feet will give you the answer of 2 for one block. Since I want to find the difference of how much longer Curiosity is compared to Sojourner, I would need to multiply 2 times 4 blocks to get a total of 8 Feet for my answer.

200

Six Men are aboard the international Space Station. There are 1/3 as many women as men aboard. How many people in all are aboard the international Space Station ?

Model three blocks representing men, which totals 6 men. Model 1 block representing women, which is 1/3 of men total. Find 1/3 of 6 to know how many women are on board 1/3 x 6/1 = 6/3 = 2 women Total people on board = 2 women plus 6 men Answer is 8 people.

300

A Light Year is the distance light travels in 1 year. A parsec is a unit of measurement equal to 3 1/4 light years. How many light years are equal to 5 parsecs ?

If you modeled this equal groups problem, you would have one bar with 5 blocks representing the 5 parsecs. We know one block represents 3 1/4 light years. To find 5 parsecs, we need to multiply 3 1/4 by 5. 3 1/4 x 5 = 16 1/4 light years

400

Objects on Jupiter weight 2 1/3 times as much as they do on Earth. A battery weights 3 pounds on Earth. How many more pounds will it weigh on Jupiter ?

Modeling this compare problem I would represent Jupiter with two blocks plus a smaller block at the end. Earth would be one block that represents 3 pounds. Looking at my model I can see the difference for Jupiter compared to Earth is 1 and 1/3 blocks. If I multiply 1 and 1/3 blocks by 3, since each block is 3 pounds, I can find my answer. 1 1/3 x 3 = 4/3 x 3/1 = 12/3 = 4 pounds

500

If I was playing a game and rolled dice with the following numbers: 2,4,5 What fractions could I create to get a smaller answer in a division problem format shown below: [ ] divided by 1 ---- --- [ ] [ ]

What is 2/5 divided by 1/4 If the number on top/Numerator is larger than the bottom number/Denominator, then it will give you a larger answer and would be incorrect.

Renaming and Simplifying

100

Rename 2/5 x 12

2 x 1/5 x 12 (can be in a different order, but same numbers)

200

Rename 3 x 6/5

3 x 6 x 1/5 Can be in a different order.

300

Rename 4 x 1 3/4 (second number is one and three fourths)

4 x (1 + 3/4) If you changed 1 3/4 to an improper fraction, then you might have this answer 4 x 7/4 renames to 4 x 7 x 1/4

400

Rename 4 3/5 into an improper fraction

4 3/5 is the same as 5/5 + 5/5 + 5/5+ 5/5 + 3/5 which equals 23/5

500

Rename 2 3/4 as an improper fraction

2 and 3/4 is the same as 4/4 + 4/4 + 3/4 which would be 11/4 as an improper fraction.

Mystery... If you DARE !

100

What does a white dove symbolize?

Peace

200

Give one example of using a Growth Mindset

Believe in yourself
Working hard at learning, even if you don't like it
Everyone can be a math person
Tell yourself you haven't learned it.... yet!
Keeping trying, even when you make mistakes.
Mistakes mean you are learning !

300

Name one Math Celebrity Mrs. Fisher has met at the MidSchoolMath Conference ?

Jo Boaler author of Mathematical Mindsets

or

Dan Meyer inventor of the 3-Act Task

400

Name three things you know about Mrs. Fisher or her family.

Mrs. Fisher can validate this one.

500

Name a music celebrity or group Mrs. Fisher has met or seen in concert.

Mrs. Fisher can validate concerts.

She has met Wierd Al Yankovic, Rockapella, 29Palms, Squeeze.