## 6th & 7th Grade Program Overview

*You probably know how to find a common denominator and maybe even add or subtract fractions. But have you ever played Fraction JEOPARDY! against your peers to find out how good your fraction skills really are? Completed a crossword puzzle where the answers are all numbers — no letters? Practiced breaking codes or creating new ones? Do you know what shape you should use for your garden? Should it be a rectangle or a square — which one will get you more vegetables — because it’s more “efficient”?*

Explore math without boundaries. It can get messy — but you’ll have fun and learn some really cool things — even though it’s math. Because math is cool.

**Who:** Recommended for both incoming 6th and 7th grade students who are seeking additional challenge.

### The SelectivePrep 6th/7th Grade Math Enrichment Program

- Is offered in a 5 day session (one week long), M-F and is 3 hours per session or 15 hours in total
- Limits class size to 20 students
- Includes hands-on workshops and exercises where students gain additional practice

**Cost: $350 for week long session**

### Program Format

Each session is divided into three parts:

**Concept Review.**Students will interactively work through problems in each topic area to ensure that the concepts are well understood.**Application.**Students will apply concepts in real life simulations or word problems to gain practical experience.**Game/Contest.**Students work through challenge questions and compete for prizes, either in teams or individually.

### 6th/7th Grade Program Syllabus

### Session 1: Fractions and Mixed Numbers Concept Review

- Adding and subtracting fractions; finding common denominators
- Multiplying and dividing fractions; the importance of canceling; what to flip, when to flip, and why
- Mixed numbers; when to change them to improper fractions and when not to; borrowing and carrying with mixed numbers
- Fractions and number sense; the meaning of increasing the denominator; comparing fractions

**Application:** Jelly Bean Business Simulation

**Game/Exercise:** Fraction Jeopardy! Students play in a Jeopardy game that draws on their knowledge of fraction rules.

### Session 2: Number Properties Concept Review

- Divisibility rules; how to tell if a number is divisible by 3, 4, 9, and 11; combining divisibility rules (e.g., is 101,004 divisible by 6?)
- Factoring; determine the factors of a given number; prime factorization (e.g., list the factors of 120, list the prime factors of 135)
- Positives and negatives; rules of addition, subtraction, multiplication, division, and exponents for signed numbers; absolute value (e.g., what is larger — (-2)
^{3}or (-2)^{4}, (-2)^{3}or (-2)5, |(-2)^{3}| or |(-2)^{5})|?) - Remainders; the meaning of remainders; remainders as an aid in pattern questions (e.g., what is the 200th term in the series a, b, c, d, e, f, g, a, b, c, d, e, f, g, …)
- Squares and cubes; introduction to exponents; common squares (e.g., how many cubes of positive integers are less than 100?)

**Application:** Divisibility Bingo. Students play a bingo game which draws on their mastery of divisibility rules.

**Game/Exercise:** Students complete an all number – no word — crossword puzzle.

### Session 3: Logic and Probability Concept Review

- Maximum/minimum; visualization; the possible and impossible (e.g., on a bookshelf every 3rd book is blue, every 4th book is green and every 5th book is red; what is the maximum number of books that could be on the shelf?)
- Symbol problems; as an introduction to algebra and functions
- Probability; simple probability; joint probability (e.g., if a pair of dice is rolled what is the probability of rolling an 8?; what is the probability of pulling a jack or a club from a deck of cards?)
- Combinations and permutations (e.g., how many ways can 8 horses line up in the starting gate?; Bill must read 3 books out of 7 books on his list; how many 3-book choices are available to him?)

**Application:** Students put their logic skills to work as they devise and break codes.

**Game/Exercise:** Students test the basic theory of probability using a deck of cards. How likely will it be to get a heart? The ace of hearts? Three of a kind?

### Session 4: Percent Concept Review

- Basic percents; the “meaning” of percents; making percents from fractions & decimals and back again; demonstrate the linkages between fractions and percents; percents over 100% and less than 1% (what is 2.3% as a decimal?)
- Simple percent questions; the basic percent formula – part = % × whole; percents as proportions (e.g., what % of 60 is 24?; 36 is 30% of what number? what is 45% of 300?)
- Advanced percentage topics; percentage increase and decrease; percent greater than or less than; picking numbers with percents; real world percent problems including percent profit and loss, sales taxes, and tips (e.g., Jane’s salary rose by 25% and is now $600 – what was her original salary; the price of an item is discounted by 20% – by what % must the discounted price rise to get back to the original price?; George buys 3 notebooks at $1.40 each. If sales tax is 5% and he pays with a $5 bill, what is his change?)

**Game/Exercise:** Using a simulation, students make investment decisions and calculate their return on investment.

### Session 5: Geometry Concept Review

- Lines and Angles; degrees around a point; degrees on one side of a line; types of angles; parallel and perpendicular lines; complementary and supplementary angles (e.g., angle A = 40°, angle B is supplementary to angle A, angle C is complementary to angle A; the average of angle B and angle C is ?)
- Triangles; degrees in a triangle; area of a triangle; properties of all triangles, isosceles, equilateral, right triangles, Pythagorean Theorem (e.g., a bird flies 6 miles east; then it flies 8 miles south; if it flies directly back to its starting point, how many miles will it fly?)
- Rectangles; area and perimeter of rectangles; area and perimeter of squares (e.g., a farmer wants to fence in 2 plots of land, both of which have an area of 36 sq. ft.; one is a square and the other has a length of 9 ft.; if fencing costs $2/foot how much more will it cost to fence the second plot?)
- Advanced Topics; regular figures, similar figures, volume and surface area (e.g., how many degrees are there in each angle of a stop sign?)

**Game/Exercise:** Students construct a scale map of the room.