options: Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Write and interpret numerical expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Gain familiarity with factors and multiples.

Work with radicals and integer exponents.

Interpret the structure of expressions.

Work with equal groups of objects to gain foundations for multiplication.

Perform arithmetic operations on polynomials.

Reason about and solve one-variable equations and inequalities.

Understand the relationship between zeros and factors of polynomials.

Generate and analyze patterns.

Use properties of operations to generate equivalent expressions.

Understand properties of multiplication and the relationship between multiplication and division.

Represent and solve problems involving multiplication and division.

Understand the connections between proportional relationships, lines, and linear equations.

Use polynomial identities to solve problems.

Solve equations and inequalities in one variable.

Work with addition and subtraction equations.

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving addition and subtraction.

Add and subtract within 20.

Understand solving equations as a process of reasoning and explain the reasoning.

Analyze patterns and relationships.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Solve systems of equations.

Write expressions in equivalent forms to solve problems.

Rewrite rational expressions.

Multiply and divide within 100.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve equations and inequalities graphically.

Understand and apply properties of operations and the relationship between addition and subtraction.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Create equations that describe numbers or relationships

Analyze and solve linear equations and pairs of simultaneous linear equations.
problem_activity: Problem 1
What is an equation of the line represented in the graph below?
[IMG]
Problem 2
Four lines were used to define the edges of the trapezoid shown below.
[IMG]
Write an equation for each line described below.
a.   Line that passes through points
$$A$$
and
$$B$$
b.   Line that passes through points
$$B$$
and
$$C$$
c.   Line that passes through points
$$C$$
and
$$D$$
d.   Line that passes through points
$$D$$
and
$$A$$
Problem 3
Optional: Play the memory
Matching Game
with linear equations and graphs. Note that this requires some advance preparation.
Directions for students:
Find a partner and clear off your desks.
Separate the cards into a pile with equations and a pile with graphs.
Turn the equation cards over and organize them into rows/columns on one desk.
Turn the graph cards over and organize them into rows/columns on another desk.
On the first person’s turn, turn over an equation card and a graph card. If the cards match, then the player gets to keep the cards. If they do not match, turn the cards over in the same spot. The turn is over.
NOTE: If the player believes she or he has a match, then the player must prove that there is a match. The other player has the option to disagree and explain why. If the other player is right (and the first player was mistaken), then the other player gets to keep the card and then take a turn.
Repeat step 5 for the second player’s turn.
The game is over when all cards have been matched. The person with the most number of pairs wins the round. Another round may be played.


correct_option_index: 14