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

Write and interpret numerical expressions.

Represent and solve problems involving addition and subtraction.

Multiply and divide within 100.

Use the four operations with whole numbers to solve problems.

Use polynomial identities to solve problems.

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

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

Write expressions in equivalent forms to solve problems.

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

Generate and analyze patterns.

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

Use properties of operations to generate equivalent expressions.

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

Solve systems of equations.

Perform arithmetic operations on polynomials.

Add and subtract within 20.

Reason about and solve one-variable equations and inequalities.

Rewrite rational expressions.

Work with radicals and integer exponents.

Understand the relationship between zeros and factors of polynomials.

Represent and solve equations and inequalities graphically.

Create equations that describe numbers or relationships

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

Interpret the structure of expressions.

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.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Work with addition and subtraction equations.

Solve equations and inequalities in one variable.

Gain familiarity with factors and multiples.

Analyze patterns and relationships.

Apply and extend previous understandings of arithmetic to algebraic expressions.
problem_activity: Problem 1
A clothing manufacturer has to use at least 1,000 yards of cotton to make room for new inventory to make shirts and pajamas. A shirt requires 1 yard of fabric, and a pair of pajamas requires 3 yards of fabric. It takes 2 hours to make a shirt and 3 hours to make a pair of pajamas, and there are 1600 hours available to make all of the clothing. Let
$$x$$
represent the number of shirts and
$$y$$
represent the number of pajamas.
What is the smallest number of pajamas the manufacturer can make and meet all of these conditions?
Problem 2
Phil and Cath make and sell boomerangs for a school event. The money they raise will go to charity. They plan to make them in two sizes: small and large.
Phil will carve them from wood.
The small boomerang takes 2 hours to carve, and the large one takes 3 hours to carve.
Phil has a total of 24 hours available for carving.
Cath will decorate them. She only has time to decorate 10 boomerangs of either size.
Phil and Cath want to make as much money for charity as they can.
The small boomerang will make $8 for charity.
The large boomerang will make $10 for charity.
How many small and large boomerangs should they make?
How much money will they then make?


correct_option_index: 21

22