Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit. Calculate the number of significant figures for an assortment of numbers.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Students will record the temperature daily, using a bar graph, color coded bars. this monthly bar graph helps students understand phenology and interpreting graphs.

Before entering first grade, young children need to have a basic understanding of measurement. They do not need to be able to use standard units of measurement, but they must be able to use the basic attributes to make comparisons in length.

This Little Farm is full of sweet farm animals! Come with Miss Penny and the KidVision Pre-K Kids as they collect eggs, measure a pony, and milk a goat. You will hear the sounds all your favorite farm animals make! It will inspire your class to sing..."Old MacDonald had a farm......" Included are links to age-appropriate lesson plans. [8:51]

Models how to solve word problems involving metric length. [5:49]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

With the assistance of a few teacher demonstrations (online animation, using a radiometer and rubbing hands), students review the concept of heat transfer through convection, conduction and radiation. Then they apply an understanding of these ideas as they use wireless temperature probes to investigate the heating capacity of different materials sand and water under heat lamps (or outside in full sunshine). The experiment models how radiant energy drives convection within the atmosphere and oceans, thus producing winds and weather conditions, while giving students the hands-on opportunity to understand the value of remote-sensing capabilities designed by engineers. Students collect and record temperature data on how fast sand and water heat and cool. Then they create multi-line graphs to display and compare their data, and discuss the need for efficient and reliable engineer-designed tools like wireless sensors in real-world applications.

Kindergarteners need a variety of experiences to ensure they build a strong foundation on a topic. This lesson gives them another opportunity to compare height, this time using themselves as the objects.

Students use next-generation air quality monitors to measure gas-phase pollutants in the classroom. They apply the knowledge they gained during the associated lesson—an understanding of the connection between air pollutants and their possible sources. Student teams choose three potential pollutant sources and predict how the monitor’s sensors will respond. Then they evaluate whether or not their predictions were correct, and provide possible explanations for any inaccuracies. This activity serves as a simple introduction to the low-cost air quality monitoring technology that students use throughout the associated activities that follow. Three student handouts are provided.

This pathway introduces the units scientists use when making measurements and how to judge and express the meaning and level of confidence in a measurement.

Gain a basic understanding of the metric system by watching this easy to understand video tutorial. Additional resources are available as part of a paid subscription service. [10:50]

This QuickTime movie presents a problem to find the area of a multi-sided shape that requires an extended response. The teacher and student discuss how to work through it together to find the solution. As you watch and listen to the teacher and student interact it helps clarify the thinking behind applying this concept.

Distributions and Variability

Type of Unit: Project

Prior Knowledge

Students should be able to:

Represent and interpret data using a line plot.
Understand other visual representations of data.

Lesson Flow

Students begin the unit by discussing what constitutes a statistical question. In order to answer statistical questions, data must be gathered in a consistent and accurate manner and then analyzed using appropriate tools.

Students learn different tools for analyzing data, including:

Measures of center: mean (average), median, mode
Measures of spread: mean absolute deviation, lower and upper extremes, lower and upper quartile, interquartile range
Visual representations: line plot, box plot, histogram

These tools are compared and contrasted to better understand the benefits and limitations of each. Analyzing different data sets using these tools will develop an understanding for which ones are the most appropriate to interpret the given data.

To demonstrate their understanding of the concepts, students will work on a project for the duration of the unit. The project will involve identifying an appropriate statistical question, collecting data, analyzing data, and presenting the results. It will serve as the final assessment.

Students collect data to answer questions about a typical sixth grade student. Students collect data about themselves, working in pairs to measure height, arm span, etc. Students discuss characteristics they would like to know about sixth grade students, adding these topics to a preset list. Data are collected and organized such that there is a class data set for each topic for future use. Students are asked to think about how this data could be represented and organized.Key ConceptsFor data to be useful, it must be collected in a consistent and accurate way. For example, for height data, students must agree on whether students should be measured with shoes on or off, and whether heights should be measured to the nearest inch, half inch, or centimeter.Goals and Learning ObjectivesGather data about sixth grade students.Consider how data are collected.

Surface Area and Volume

Type of Unit: Conceptual

Prior Knowledge

Students should be able to:

Identify rectangles, parallelograms, trapezoids, and triangles and their bases and heights.
Identify cubes, rectangular prisms, and pyramids and their faces, edges, and vertices.
Understand that area of a 2-D figure is a measure of the figure's surface and that it is measured in square units.
Understand volume of a 3-D figure is a measure of the space the figure occupies and is measured in cubic units.

Lesson Flow

The unit begins with an exploratory lesson about the volumes of containers. Then in Lessons 2–5, students investigate areas of 2-D figures. To find the area of a parallelogram, students consider how it can be rearranged to form a rectangle. To find the area of a trapezoid, students think about how two copies of the trapezoid can be put together to form a parallelogram. To find the area of a triangle, students consider how two copies of the triangle can be put together to form a parallelogram. By sketching and analyzing several parallelograms, trapezoids, and triangles, students develop area formulas for these figures. Students then find areas of composite figures by decomposing them into familiar figures. In the last lesson on area, students estimate the area of an irregular figure by overlaying it with a grid. In Lesson 6, the focus shifts to 3-D figures. Students build rectangular prisms from unit cubes and develop a formula for finding the volume of any rectangular prism. In Lesson 7, students analyze and create nets for prisms. In Lesson 8, students compare a cube to a square pyramid with the same base and height as the cube. They consider the number of faces, edges, and vertices, as well as the surface area and volume. In Lesson 9, students use their knowledge of volume, area, and linear measurements to solve a packing problem.

Lesson OverviewStudents find the area of a parallelogram by rearranging it to form a rectangle. They find the area of a trapezoid by putting together two copies of it to form a parallelogram. By doing these activities and by analyzing the dimensions and areas of several examples of each figure, students develop and understand area formulas for parallelograms and trapezoids.Key ConceptsA parallelogram is a quadrilateral with two pairs of parallel sides. The base of a parallelogram can be any of the four sides. The height is the perpendicular distance from the base to the opposite side.A trapezoid is a quadrilateral with exactly one pair of parallel sides. The bases of a trapezoid are the parallel sides. The height is the perpendicular distance between the bases.You can cut a parallelogram into two pieces and reassemble them to form a rectangle. Because the area does not change, the area of the rectangle is the same as the area of the parallelogram. This gives the parallelogram area formula A = bh.You can put two identical trapezoids together to form a parallelogram with the same height as the trapezoid and a base length equal to the sum of the base lengths of the trapezoid. The area of the parallelogram is (b1 + b2)h, so the area of the trapezoid is one-half of this area. Thus, the trapezoid area formula is A = 12(b1 + b2)h.Goals and Learning ObjectivesDevelop and explore the formula for the area of a parallelogram.Develop and explore the formula for the area of a trapezoid.

Lesson OverviewStudents find the area of a triangle by putting together a triangle and a copy of the triangle to form a parallelogram with the same base and height as the triangle. Students also create several examples of triangles and look for relationships among the base, height, and area measures. These activities lead students to develop and understand a formula for the area of a triangle.Key ConceptsTo find the area of a triangle, you must know the length of a base and the corresponding height. The base of a triangle can be any of the three sides. The height is the perpendicular distance from the vertex opposite the base to the line containing the base. The height can be found inside or outside the triangle, or it can be the length of one of the sides.You can put together a triangle and a copy of the triangle to form a parallelogram with the same base and height as the triangle. The area of the original triangle is half of the area of the parallelogram. Because the area formula for a parallelogram is A = bh, the area formula for a triangle is A = 12bh.Goals and Learning ObjectivesDevelop and explore the formula for the area of a triangle.

Algebraic Reasoning

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Add, subtract, multiply, and divide rational numbers.
Evaluate expressions for a value of a variable.
Use the distributive property to generate equivalent expressions including combining like terms.
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?
Write and solve equations of the form x+p=q and px=q for cases in which p, q, and x are non-negative rational numbers.
Understand and graph solutions to inequalities x<c or x>c.
Use equations, tables, and graphs to represent the relationship between two variables.
Relate fractions, decimals, and percents.
Solve percent problems included those involving percent of increase or percent of decrease.

Lesson Flow

This unit covers all of the Common Core State Standards for Expressions and Equations in Grade 7. Students extend what they learned in Grade 6 about evaluating expressions and using properties to write equivalent expressions. They write, evaluate, and simplify expressions that now contain both positive and negative rational numbers. They write algebraic expressions for problem situations and discuss how different equivalent expressions can be used to represent different ways of solving the same problem. They make connections between various forms of rational numbers. Students apply what they learned in Grade 6 about solving equations such as x+2=6 or 3x=12 to solving equations such as 3x+6=12 and 3(x−2)=12. Students solve these equations using formal algebraic methods. The numbers in these equations can now be rational numbers. They use estimation and mental math to estimate solutions. They learn how solving linear inequalities differs from solving linear equations and then they solve and graph linear inequalities such as −3x+4<12. Students use inequalities to solve real-world problems, solving the problem first by arithmetic and then by writing and solving an inequality. They see that the solution of the algebraic inequality may differ from the solution to the problem.

Students use algebraic expressions and equations to represent rules of thumb involving measurement. They use properties of operations and the relationships between fractions, decimals, and percents to write equivalent expressions.Key ConceptsExpressions and equations are different. An expression is a number, a variable, or a combination of numbers and variables. Some examples of expressions are:74x5a + b3(2m + 1)In Grade 7, the focus is on linear expressions. A linear expression is a sum of terms that are either rational numbers or a rational number times a variable (with an exponent of either 0 or 1). If an expression contains a variable, it is called an algebraic expression. To evaluate an expression, each variable is replaced with a given value.Equivalent expressions are expressions for which a given value can be substituted for each variable and the value of the expressions are the same.An equation is a statement that two expressions are equal. An equation can be true or false. To solve an equation, students find the value of the variable that makes the equation true.Students solve an equation that involves finding 10% of a number. They see that finding 10% of the number is the same as finding 0.1 of the number, or finding 110 of the number.Goals and Learning ObjectivesWrite expressions and equations to represent real-world situations.Evaluate expressions for given values of a variable.Use properties of operations to write equivalent expressions.Solve one-step equations.Check the solution to an equation.