Solve Problems by Graphing
Solving problems by graphing is a Grade 5 math skill in enVision Mathematics, Chapter 14: Graph Points on the Coordinate Plane. Students represent two related quantities as ordered pairs (x, y), plot them on a coordinate plane, and extend the pattern to find unknown values. Graphing makes relationships between quantities visual, allowing students to answer questions by reading or extrapolating from the graph.
Key Concepts
Property Real world problems involving two related quantities, $x$ and $y$, can be solved by graphing. The relationship is represented by a set of ordered pairs $(x, y)$, which are plotted on a coordinate plane. The resulting graph can be used to find unknown values by extending the pattern.
Examples A food truck sells tacos for 3 dollars each. The relationship between the number of tacos bought ($x$) and the total cost ($y$) can be graphed. Using the graph, you can find the cost of 5 tacos by finding the $y$ value when $x=5$. The point $(5, 15)$ on the graph shows the cost is 15 dollars. A plant is 5 cm tall and grows 2 cm each week. Graph the relationship between the number of weeks ($x$) and the plant''s height ($y$). To find the plant''s height after 4 weeks, locate $x=4$ on the graph and find the corresponding $y$ value, which would be at the point $(4, 13)$.
Explanation This skill involves translating a word problem into a visual graph to find a solution. First, identify the two quantities that change and assign them to the $x$ and $y$ axes. Then, create a table of values based on the rule in the problem and plot these ordered pairs as points. Finally, use the pattern of the points on the graph to find the answer to the question asked in the problem.
Common Questions
How do you solve a problem by graphing?
Create ordered pairs from the problem data, plot them on a coordinate plane, then extend the pattern or read the graph to find unknown values.
Why is graphing useful for solving word problems?
Graphs make the relationship between two quantities visual. You can find unknown values by looking at the graph rather than calculating.
How do you find a value from a graph?
Locate the known coordinate on the appropriate axis, trace across or up to the plotted line, then read the corresponding value on the other axis.
Where is solving problems by graphing taught in enVision Grade 5?
Chapter 14: Graph Points on the Coordinate Plane in enVision Mathematics, Grade 5.
What are real-world examples of solving problems by graphing?
Examples include finding the cost of multiple items when the cost per item is known, or determining distance over time when the speed is constant.