options: Write expressions in equivalent forms to solve problems.

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

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

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

Reason about and solve one-variable equations and inequalities.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Write and interpret numerical expressions.

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

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

Perform arithmetic operations on polynomials.

Gain familiarity with factors and multiples.

Work with radicals and integer exponents.

Solve systems of equations.

Rewrite rational expressions.

Analyze patterns and relationships.

Use the four operations with whole numbers to solve problems.

Create equations that describe numbers or relationships

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

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

Work with addition and subtraction equations.

Understand the relationship between zeros and factors of polynomials.

Represent and solve problems involving addition and subtraction.

Use polynomial identities to solve problems.

Generate and analyze patterns.

Use properties of operations to generate equivalent expressions.

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

Multiply and divide within 100.

Solve equations and inequalities in one variable.

Represent and solve equations and inequalities graphically.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Represent and solve problems involving multiplication and division.

Add and subtract within 20.

Interpret the structure of expressions.
problem_activity: Problem 1
Julia, Keller, and Isreal are volunteer firefighters. On Saturday, the volunteer fire department held its annual coin drop fundraiser at a streetlight. After one hour, Keller had collected $42.50 more than Julia, and Isreal had collected $15 less than Keller. The three firefighters collected $125.95 in total. How much did each person collect?
Problem 2
Your parents are redecorating the dining room and want to place two rectangular pictures, each measuring 25 inches across, on the wall, which measures
$${10 {2\over3}}$$
feet long. They want to place the pictures so that the distance between the pictures and the distances from each picture to the end of the wall are the same, as shown in the diagram below.
[IMG]
Determine the distance each picture should be placed from the ends of the wall. Explain the strategy that you used.
Problem 3
Three toothpick configurations are shown in the chart below.
[IMG]
a.   Extend the pattern to complete the chart.
b.   How many toothpicks will be in the 10th design?
c.   Write an expression to represent the number of toothpicks in the
$$n$$
th design.
d.   Which design will have 175 toothpicks? Write and solve an equation.


correct_option_index: 8