options: Gain familiarity with factors and multiples.

Use the four operations with whole numbers to solve problems.

Use properties of operations to generate equivalent expressions.

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

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

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

Work with addition and subtraction equations.

Use polynomial identities to solve problems.

Represent and solve problems involving addition and subtraction.

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

Understand the relationship between zeros and factors of polynomials.

Write and interpret numerical expressions.

Create equations that describe numbers or relationships

Multiply and divide within 100.

Write expressions in equivalent forms to solve problems.

Add and subtract within 20.

Reason about and solve one-variable equations and inequalities.

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

Analyze patterns and relationships.

Represent and solve equations and inequalities graphically.

Represent and solve problems involving multiplication and division.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Perform arithmetic operations on polynomials.

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

Generate and analyze patterns.

Solve systems of equations.

Rewrite rational expressions.

Interpret the structure of expressions.

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

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

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

Work with radicals and integer exponents.

Solve equations and inequalities in one variable.

Represent and analyze quantitative relationships between dependent and independent variables.
problem_activity: Problem 1
Two students are presented with the challenge of adding
$${2.5\times10^3}$$
and
$${1.3\times10^4}$$
. They have just learned how to multiply numbers in scientific notation, and they try out using similar strategies. They get two possible answers:
$${3.8\times10^4}$$
OR
$${3.8\times10^7}$$
a.   Explain or show to the students how both of the answers are incorrect.
b.   Why will the strategies used when multiplying numbers in scientific notation not work when adding?
c.   What are some strategies that can be used to solve this problem? Find the sum.
Problem 2
The Great Lakes are a series of freshwater lakes located on the US and Canadian border. Lake Superior has the greatest volume of water with
$${3.12\times10^{15}}$$
gallons of water. The smallest lake, by volume of water, is Lake Ontario with
$${4.26\times10^{14}}$$
gallons of water.
How many more gallons of water are in Lake Superior than in Lake Ontario?
Problem 3
A water molecule is made up of 2 hydrogen atoms and 1 oxygen atom, represented as H
2
O. One hydrogen atom has a mass of
$${1.7\times10^{-27}}$$
kg, and one oxygen atom has a mass of
$${2.7\times10^{-26}}$$
kg.
What is the total mass of a single water molecule?


correct_option_index: 31