Lighthouse Initiative for Texas Classrooms

TEKS: Grade 7

Read an introduction to Texas Essential Knowledge and Skills charts.

TEKS Examples Commentary

111.23. MATHEMATICS, GRADE 7.

7.1 Number, operation, and quantitative reasoning. The student represents and uses numbers in a variety of equivalent forms.

(A) compare and order integers and positive rational numbers;

(B) convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator; and

(C) represent squares and square roots using geometric models.

 

 

 

 

 

 

7.2 Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justify solutions.

(A) represent multiplication and division situations involving fractions and decimals with models including concrete objects, pictures, words, and numbers;

(B) use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals;

(C) use models such as concrete objects, pictorial models, and number lines, to add, subtract, multiply, and divide integers and connect the actions to algorithms;

 

 

 

 

 

 

(D) use division to find unit rates and ratios in proportional relationships such as speed, density, price, recipes, and student-teacher ratio;

Using a map or road atlas, choose two cities that are at least 700 miles apart. Determine the distance between them. Determine how much time that you would save driving from one city to another at 70 miles per hour instead of 55 mph. If your car averages 27 miles per gallon when traveling 55 mph, determine the cost of the trip at this speed. If your car averages 22 miles per gallon when traveling at 70 mph, determine the cost of the trip at this speed. Compare the two costs. Using this data, write a paragraph describing which speed is best in terms of time, cost.

The diameter of the earth is about 8,000 miles. What would your speed be in miles per hour if you took 80 days to circumnavigate the earth at the equator?

A variation of this problem would be to choose two cities that are relatively close together, 40 miles or less.

This activity was adapted from Real Life Math: Algebra, Walch Education, page 188.

(E) simplify numerical expressions involving order of operations and exponents;

(F) select and use appropriate operations to solve problems and justify the selections; and

(G) determine the reasonableness of a solution to a problem.

 

 

 

 

 

 

7.3 Patterns, relationships and algebraic thinking. The student solves problems involving direct proportional relationships.

(A) estimate and find solutions to application problems involving percent; and

 

 

 

 

 

 

(B) estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units.

 

 

 

You are building your dream home. It is time now to determine the costs of your flooring. You have found a carpet for the bedrooms and the hallways. Because of the amount of foot traffic in the kitchen, entryway, and bathrooms, you have chosen a ceramic tile. In the living room and dining room, you want a hardwood floor. Using these costs, determine the total cost of flooring for your home.

Carpet costs $20.95 per sq. yard. Tile, $5.50 per sq foot. Hardwood flooring is $9.00 per sq foot.

TEKS, Grade 7, Figure 1

 

 

 

 

 

7.4 Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal and symbolic form.

(A) generate formulas involving conversions, perimeter, area, circumference, volume, and scaling;












1. Distribute to your students circular lids, cans and other items of various sizes. Have the students measure the circumference and diameter of these items. Record the data in a table. Determine the relationship between the diameter and the circumference. Graph the data using the diameter as the independent variable. What is the slope of the line? Write an equation that expresses the relationship between the diameter and the circumference.

2. Roll a 5-inch by 8-inch index card into a cylinder by taping the shorter sides together. Roll another 5 x 8 index card into a cylinder by taping the long sides together. Use rice to compare their volumes. Does one hold more than the other? What is the volume of each? Write a summary sentence that explains what this activity shows.












NCTM Addenda Series, Grades 5-8, discusses this problem (Patterns and Functions and Measurement in the Middle Grades).

(B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling; and

(C) use words and symbols to describe the relationship between the terms in an arithmetic sequence (with a constant rate of change) and their positions in the sequence.

   

 

 

   

 

 

7.5 Patterns, relationships, and algebraic thinking. The student uses equations to solve problems.

(A) use concrete and pictorial models to solve equations and use symbols to record the actions; and

(B) formulate problem situations when given a simple equation and formulate an equation when given a problem situation.

7.6 Geometry and spatial reasoning. The student compares and classifies two- and three-dimensional figures using geometric vocabulary and properties.

(A) use angle measurements to classify pairs of angles as complementary or supplementary;

(B) use properties to classify triangles and quadrilaterals;

(C) use properties to classify three-dimensional figures, including pyramids, cones, prisms, and cylinders; and

(D) use critical attributes to define similarity.

 

 

 

 

 

 

7.7 Geometry and spatial reasoning. The student uses coordinate geometry to describe location on a plane.

(A) locate and name points on a coordinate plane using ordered pairs of integers; and

(B) graph reflections across the horizontal or vertical axis and graph translations on a coordinate plane.

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

(A) sketch three-dimensional figures when given the top, side, and front views;

(B) make a net (two-dimensional model) of the surface area of a three-dimensional figure; and

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

7.9 Measurement. The student solves application problems involving estimation and measurement.

(A) estimate measurements and solve application problems involving length (including perimeter and circumference) and area of polygons and other shapes;

(B) connect models for volume of prisms (triangular and rectangular) and cylinders to formulas of prisms (triangular and rectangular) and cylinders; and

(C) estimate measurements and solve application problems involving volume of prisms (rectangular and triangular) and cylinders.






















































A dining room is 12 feet by 15 feet. Design a circular table, so that twelve chairs, each 18 inches wide, will fit around the table. Allow at least 8 inches between the chairs. Explain how you determined the dimensions of the table. Draw a scale model of the dining room and your table. Is the table a reasonable size? Is there sufficient room for people to sit comfortably at this table in this room?

 

 

 

7.10 Probability and statistics. The student recognizes that a physical or mathematical model can be used to describe the experimental and theoretical probability of real-life events.

(A) construct sample spaces for simple or composite experiments; and

(B) find the probability of independent events.

7.11 Probability and statistics. The student understands that the way a set of data is displayed influences its interpretation.

(A) select and use an appropriate representation for presenting and displaying relationships among collected data, including line plot, line graph, bar graph, stem and leaf plot, circle graph, and Venn diagrams, and justify the selection; and

(B) make inferences and convincing arguments based on an analysis of given or collected data.

7.12 Probability and statistics. The student uses measures of central tendency and range to describe a set of data.

(A) describe a set of data using mean, median, mode, and range; and

(B) choose among mean, median, mode, or range to describe a set of data and justify the choice for a particular situation.

 

 

 

 

 

 

7.13 Underlying processes and mathematical tools. The student applies Grade 7 mathematics to solve problems connected to everyday experiences, investigations in other disciplines and activities inside 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.

7.14 Underlying processes and mathematical tools. The student communicates about Grade 7 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.

 

 

 

 

 

 

7.15 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.

 

 

 

 

[printer-friendly]