# Level 2 - Math & Problem Solving

Our **Level 2** Math & Problem Solving course typically targets students in **Grades 6 through 8.** However, students at other grade levels may be placed in Level 2 if they meet all prerequisites for this level, and/or have successfully completed Level 1. The major emphasis at this level is shifting from learning how to understand a problem and recognizing different problem solving strategies to **techniques of problem solving.** The level of problem complexity in Level 2 is visibly higher than in Level 1.

Level 2 instruction includes, but is not limited to:

###### Math

- Negative numbers
- Four operations (+,-, x, /) on integers
- Four operations on positive and negative numbers
- Algebraic Equations
- Order of operations involving positive and

negative numbers - Algebra: simple problems with one variable
- Proportions

###### Memory development

- Brain Power memory technique

###### Higher-Level Logic and Problem Solving Strategies

###### Logic and Problem Solving Strategies

- Reading comprehension
- Modeling problems and simplifying them
- Forward solving strategies
- Backwards solving strategies
- Venn diagrams

- Logical charts
- Organized / Systematic list
- Problems on lowest common multiple
- Logical trees
- Problem decomposition

**Prerequisite for Level 2**: ease of operating on decimals, fractions, and percent; basic knowledge of problem solving strategies; completion of the Level 1 OR successful completion of interview (for new students).

##### Sample problems

Jordan and Jerald participate in a running competition. Jerald is taller than Jordan and he is faster. When Jerald ran 6/7 of the distance, Jordan ran 3/4 of the distance. At that time Jerald was 9 meters ahead of Jordan. What is the distance in this running competition?

Jeremy is organizing apples and oranges on the store’s shelves. When he removed one apple from the shelf, he noticed that the number of remaining apples on the shelf was 1/7 of the fruits on the shelf. After he returned this apple to the shelf, he removed 2 oranges and noticed that this time that the number of apples was 1/5 of the fruits on the shelf. How many apples and how many oranges are on the shelf?

**Solve**:

- 2.2(4.3 – X) – 12 = 3.1(1.3X +6) – 1.42
- 3X – 7(1.5X -2) = 2 – 2(5X + 4)
- 8 – | -7 + 5| – | -6| =
- 15 – 4X < 6(2 – X) + 3

Masha had lots of money in $20 bills and in $50 bills. The number of $50 bills was 5 more than the number of $20 bills. With this money, Masha bought a nice leather jacket for $180 and a picture frame for $72. The rest of her money she donated to the cancer research project.

How many $20 bills did Masha have initially, if she donated $838 to the cancer research project?

In triangle ABC, median line BD from the vertex B splits side AC into two equal segments AD and DC. Find value of angle B in degrees if AD = DC = BD. (Make your own drawing for this problem).