Lighthouse Initiative for Texas Classrooms

TEKS: Grade 8

Read an introduction to Texas Essential Knowledge and Skills charts.

TEKS Examples Commentary

111.24 MATHEMATICS, GRADE 8

8.1 Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations.

(A) compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals;

(B) select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships;

(C) approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (π, √2); and

 

 

 

 

 

 

(D) express numbers in scientific notation, including negative exponents, in appropriate problem situations.

 

 

 

Negative exponents should be introduced as a way of expressing division.

8.2 Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions.

(A) select appropriate operations to solve problems involving rational numbers and justify the selections;

(B) use appropriate operations to solve problems involving rational numbers in problem situations;

(C) evaluate a solution for reasonableness; and

(D) use multiplication by a constant factor (unit rate) to represent proportional relationships.

8.3 Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems.

(A) compare and contrast proportional and non-proportional linear relationships; and

 

 

 

 

 

 

(B) estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.

1. Josh's father took him and four of his friends to San Antonio to watch a Spurs basketball game. The 126-mile drive took him 1 hour and 40 minutes and used 5 gallons of gas for a cost of $5.85. Use unit analysis to calculate each of the following for the entire trip. Make sure you show all your work.

a. miles per hour
b. miles per gallon
c. dollars per hour
d. dollars per gallon
e. dollars per passenger
f. yards per second
g. feet per second
h. cents per mile
i. cents per minute
j. miles per dollar
k. gallons per hour
l. passenger miles per gallon
m. cents per passenger miles

Students should write a sentence (using correct units) interpreting the meaning of each of their answers.

For c, for example, a student might write, “This is the amount of money, in dollars, it takes to pay for one hour of their trip.”

8.4 Patterns, relationships, and algebraic thinking. The student makes connections among various representations of a numerical relationship.

Figure Number Number of Tiles
1 1
2 3
3 6
4 10

Mathematics, Grade 8, Figure 1

a. Using the same pattern, how many tiles would be needed to build figure 10? Explain.
b. Construct a graph using your table. Be sure to label and scale your axes.
c. Write an equation that will give you the number of tiles for any given figure number.

 

 

 

8.5 Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions and solve problems.

 

 

 

 

 

 

(A) predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations; and

U.R.Online charges $17 per month plus 35 cents per hour for Internet service. Complete a table to show possible costs.

 

 

 

 

 

 

Hours Process Total Cost Cost per Hour
       
       
       
       
       

a. What are the only values that are appropriate for the first column?
b. Graph the data that compares the hours and cost per hour. Describe the graph as the number of hours increase. For which values of hours does it cost less than a dollar per hour to use the Internet?
c. Write an equation that describes the monthly cost of Internet service in terms of hours used.
d. If you are allowed to spend no more than $20 on Internet service, what is the maximum number of hours you are allowed on the Internet? Is this sufficient or do you need to look for another Internet provider? Explain your answer.

 

 

 

(B) find and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change)

8.6 Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense.

(A) generate similar figures using dilations including enlargements and reductions; and

(B) graph dilations, reflections, and translations on a coordinate plane.

 

 

 

 

 

 

8.7 Geometry and spatial reasoning. The student uses geometry to model and describe the physical world.

(A) draw three dimensional figures from different perspectives;

(B) use geometric concepts and properties to solve problems in fields such as art and architecture;

(C) use pictures or models to demonstrate the Pythagorean Theorem; and

(D) locate and name points on a coordinate plane using ordered pairs of rational numbers.

8.8 Measurement. The student uses procedures to determine measures of three-dimensional figures.

(A) find lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (two dimensional models);

(B) connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects; and

(C) estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume.

8.9 Measurement. The student uses indirect measurement to solve problems.

(A) use the Pythagorean Theorem to solve real-life problems; and

(B) use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements.

 

 

 

 

 

 

8.10 Measurement. The student describes how changes in dimensions affect linear, area, and volume measures.

 

 

 

 

 

 

(A) describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally; and

(B) describe the resulting effect on volume when dimensions of a solid are changed proportionally.

Students will build the unit dog using thirteen snap cubes and calculate his surface area and volume. Then students will work in pairs to construct from graph paper run on tag board, a dog with dimensions twice, triple, quadruple, or quintuple the original dog. They will calculate surface area and volume for their dog. The information for all groups will be collected, and the class will discuss the resulting effects on area and volume.

Mathematics, Grade 8, Figure 2

The ratio of an animal's volume to surface area determines the biome in which they live. High ratios live in colder climates while lower ratios reside in warmer climates. This makes a nice interdisciplinary activity with a life science class.

8.11 Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions.

(A) find the probabilities of dependent and independent events;

(B) use theoretical probabilities and experimental results to make predictions and decisions; and

 

 

 

 

 

 

(C) select and use different models to simulate an event.

Our assignment is to make a reasonable prediction about the number of goldfish crackers that are in a large bowl. This activity will use sampling techniques to estimate the population of a certain species within a defined area.

Count out 200 goldfish crackers from your population of goldfish in your bowl and replace them with tagged (parmesan or pretzel) fish. Release these fish into the lake (bowl). Each team of students will use a net (small paper cup) to capture some fish. They will count the total number of fish in their sample and how many of the fish are tagged. They should return their fish to the lake before the next team takes their sample. Each team will estimate the total number of fish in the lake (bowl) using only their data, and then they will pool the class data to make another estimate.

Students should give a written explanation about the differences between their estimates using only their data and then the class's pooled data.

The number of tagged fish needs to be between 10% and 30% of the total population in order to make an accurate prediction. In the video, The Challenge of the Unknown, there is a segment that deals with this experiment. The NCTM Addenda Series, Grades 5-8: Understanding Rational Numbers and Proportions, pages 57-60 describes this activity in detail.

(B) draw conclusions and make predictions by analyzing trends in scatter plots; and

Have students collect data on height vs. shoe size. Record the data in a table, plot the data on graph paper, and then determine a line of best fit. Since the same scale does not measure shoe sizes for males and females, you should separate the data by gender. After the data is collected and graphed, students should describe the data. What does the graph suggest? Is there a strong correlation between height and shoe size? If so, is the correlation positive or negative? Draw a line of best fit. Graph your height and shoe size on that line. How does your actual height and shoe size compare to the predicted shoe size for your height? Analyze the data using back-to-back stem plots or parallel box plots. What different information do these graphs provide?

A complete description of this activity is provided in the NCTM Addenda Series, Grades 9-12: Connecting Mathematics, pages 21-23, 26-29. This introduces the AP* Statistics concepts of correlation and linearity in bivariative data.

(C) select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams with and without the use of technology.

 

 

 

 

8.13 Probability and statistics. The student evaluates predictions and conclusions based on statistical data.

(A) evaluate methods of sampling to determine validity of an inference made from a set of data; and

(B) recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.

8.14 Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.

(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

(B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;

(C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing, and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and

(D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.

8.15 Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models.

(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and

(B) evaluate the effectiveness of different representations to communicate ideas.

8.16 Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions.

(A) make conjectures from patterns or sets of examples and non- examples; and

(B) validate his/her conclusions using mathematical properties and relationships.

 

 

 

 

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