options: Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
problem_activity: Problem 1
Consider the equation
$${ {|x|=5}}$$
.
This can be thought of as a system of equations, where
$${f(x)=\left | x \right |}$$
$${{g(x)}=5}$$
and
$${f(x)={g(x)}}$$
Graph
$${f(x) }$$
and
$${g(x)}$$
in the coordinate plane. Based on the graph, what are the solutions to
$${|x|=5}$$
?
Problem 2
For each absolute value equation below, answer the questions that follow.
$${|x|=-4}$$
$${ |x|=0}$$
$${ |x|=4}$$
How many solutions are there for
$$x$$
in each equation?
Thinking of each equation as two equal functions (similar to Anchor Problem #1), what does each one look like in the coordinate plane? Where do you see the solution(s)?
Problem 3
Solve each absolute value equation algebraically and verify the solution graphically.
$${|x+2|=8}$$
$${|x|+2=8}$$
$${|x+2|+1=0}$$


correct_option_index: 5

6