## Ch. 5 Extensions

**Ch. 5.1 Replacement Homework**

Replaces: 5.1.1 and 5.1.2

**I need to just see your problem solving process, evidence of your work, and justification of your solution. The justification could be in the form of a written reflection or explanation or a mathematical check of your solution.**

__Full Credit:__Here are the two questions. Both of them can be solved in a variety of ways, but I challenge you to use a Bar Model, or a visual picture to help find the solutions. This is a frequent problem solving method used in Singapore Math and a useful strategy for many of the problems we will see this chapter.

1. There are 600 children on a field. 30% of them were boys. After 5 teams of boys join the children on the field, the percentage of children who were boys increased to 40%. How many boys were there in the 5 teams altogether?

2. The ratio of the amount of turkey to the amount of chicken at the grocery store was 8:3 in the morning. By the end of the day, 14 pounds of turkey had been sold. The ratio of the amount of turkey to the amount of turkey was now 3:

a. How many pounds of turkey did the grocery store have in the morning?

b. How many pounds of chicken did the grocery store have in the morning?

We have also started a blog for us to use to share questions, and provide feedback as we solve these problems. Check it out!

**Ch. 5.2 Replacement Homework**

Replaces: 5.2.1 to 5.2.6

**Part 1:**

**Puzzle Investigation 5 (PI-5): Polynominoes!**

Go to the on-line textbook and click on the "References" tab and go to PI-05: Polyominoes! Look at the instructions on how to do the Puzzle Investigation and expectations. You may explain your reasoning in a Google document, digital presentation (ex. PowerPoint, Prezi, video), or poster. Here is the rubric for Puzzle Investigations.

**Part 2: How many Combinations?**

Middle school can be stressful, especially in 6th grade when you first got lockers! A combination lock uses three numbers from 0 to 39. It opens when the numbers are dialed in a particular order: right, left, right. How many possible combinations are there?

**Ch. 5.3 Replacement Homework**

Replaces: 5.3.1 to 5.3.5

**I need to just see your problem solving process, evidence of your work, and justification of your solution. The justification could be in the form of a written reflection or explanation or a mathematical check of your solution.**

__Full Credit:__**Part 1: It's not fair!**

Two players each roll an ordinary six-sided die. Of the two numbers showing, the smaller is subtracted from the larger. If the difference is 0, 1, or 2, player A gets 1 point. If the difference is 3, 4 , or 5, Player B gets 1 point. The game ends after 12 rounds. The player with the most points wins the game. Is this game fair?

**Part 2:**

**Two Kids with the Same Initials?**

How many students would have to be in a school before it was guaranteed to contain at least two people with the same first and last initial? Will Hall Middle School always have at least two kids with the same initials?