options: Solve systems of equations.

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

Work with addition and subtraction equations.

Use polynomial identities to solve problems.

Write and interpret numerical expressions.

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

Use properties of operations to generate equivalent expressions.

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

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

Add and subtract within 20.

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

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

Gain familiarity with factors and multiples.

Work with radicals and integer exponents.

Create equations that describe numbers or relationships

Represent and solve equations and inequalities graphically.

Write expressions in equivalent forms to solve problems.

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Generate and analyze patterns.

Represent and solve problems involving multiplication and division.

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

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

Solve equations and inequalities in one variable.

Rewrite rational expressions.

Multiply and divide within 100.

Represent and analyze quantitative relationships between dependent and independent variables.

Reason about and solve one-variable equations and inequalities.

Use the four operations with whole numbers to solve problems.

Understand the relationship between zeros and factors of polynomials.

Perform arithmetic operations on polynomials.

Interpret the structure of expressions.
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: 1