The purpose of this task is for students to find different pairs of numbers that sum to 4.
The purpose of this task is to assess a student's ability to compute and interpret an expected value. Notice that interpreting expected value requires thinking in terms of a long-run average.
The purpose of this game is to help students think flexibly about numbers and operations and to record multiple operations using proper notation.
This Nrich problem requires a sound understanding of the relationship between part and whole. It could be used as part of a lesson on finding fractions of numbers and quantities.
Unit 8: Data Sets and Distributions
Lesson 16: Box Plots
In this lesson, students use the five-number summary to construct a new type of data display: a box plot. Similar to their first encounter with the median, students are introduced to the structure of a box plot through a kinesthetic activity. Using the class data set that contains the numbers of letters in their names (from an earlier lesson), they first identify the numbers that make up the five-number summary. Then, they use their numbers to position themselves on a number line on the ground, and are guided through how a box plot would be constructed with them as the data points.
Later, students draw and make sense of the structure of a box plot on paper (MP7). They notice that, unlike the dot plot, it is not possible to know all the data points from a box plot. They understand that the box plot summarizes a data set by showing the range of the data, where the middle half of the data set is located, and how the values are divided into quarters by the quartiles.
Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things. Students then consider why consumer goods generally aren't packaged in cube-shaped boxes, even though they would require less material to produce and ultimately, less waste to discard. To display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. The activities involved provide valuable experience in problem solving with spatial-visual relationships.
Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things. Students then consider why consumer goods generally aren't packaged in cube-shaped boxes, even though they would require less material to produce and ultimately, less waste to discard. To display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. The activities involved provide valuable experience in problem solving with spatial-visual relationships.
To display the results from the previous activity, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. They problem solve and apply their understanding of see-saws and lever systems to create balanced mobiles.
This instructional task requires students to figure out word problems that require thinking in base 10.
Using scrap metal and spare parts, William Kamkwamba created a windmill to harness the wind and bring electricity and running water to his Malawian village. The resource includes a lesson plan/book card, a design challenge, and copy of a design thinking journal that provide guidance on using the book to inspire students' curiosity for design thinking. Maker Challenge: Develop a way to harness the wind by designing with Strawbees.
A document is included in the resources folder that lists the complete standards-alignment for this book activity.
Ralph Baer’s family fled Nazi Germany for the US when he was a child. Using wartime technology, Baer thought outside the box and transformed the television into a vehicle for gaming. His invention was the birth of the first home console, the Odyssey, a precursor to the Atari gaming system. The resource includes a lesson plan/book card, a design challenge, and copy of a design thinking journal that provide guidance on using the book to inspire students' curiosity for design thinking. Maker Challenges: (1) Think outside the box. What’s something you use everyday, but not for its “intended” purpose? Examples: A broom to clean the snow off your car windshield, a trash bag as a sled. Now, think of a problem you might have at school, home, et al. Invent an item that would solve this problem. (2) Let’s think outside the box! Design the latest and greatest technology for kids to hit the market! Make it the *most* fun anyone has ever had. You may NOT use anything on the market - any technology currently on the market is off limits. Use your imagination, do not put limitations on it, and be as creative as you can. (3) Use household items to create a prototype of your new invention.
A document is included in the resources folder that lists the complete standards-alignment for this book activity.
Students use addition or subtraction to solve these types of word problems.
This word problem has 10 possible solutions.
Learn about how coins are made and to identify the coins through videos and games.
This is a look at how coins and bills are produced along with some practice with identifying and calculating using money.
This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.
The purpose of this task is to assess a student's ability to explain the meaning of independence in a simple context.
This short text is designed more for self-study or review than for classroom use; full solutions are given for nearly all the end-of-chapter problems. For a more traditional text designed for classroom use, see Fundamentals of Calculus (http://www.lightandmatter.com/fund/). The focus is mainly on integration and differentiation of functions of a single variable, although iterated integrals are discussed. Infinitesimals are used when appropriate, and are treated more rigorously than in old books like Thompson's Calculus Made Easy, but in less detail than in Keisler's Elementary Calculus: An Approach Using Infinitesimals. Numerical examples are given using the open-source computer algebra system Yacas, and Yacas is also used sometimes to cut down on the drudgery of symbolic techniques such as partial fractions. Proofs are given for all important results, but are often relegated to the back of the book, and the emphasis is on teaching the techniques of calculus rather than on abstract results.
This short text is designed more for self-study or review than for classroom use; full solutions are given for nearly all the end-of-chapter problems. For a more traditional text designed for classroom use, see Fundamentals of Calculus (http://www.lightandmatter.com/fund/). The focus is mainly on integration and differentiation of functions of a single variable, although iterated integrals are discussed. Infinitesimals are used when appropriate, and are treated more rigorously than in old books like Thompson's Calculus Made Easy, but in less detail than in Keisler's Elementary Calculus: An Approach Using Infinitesimals. Numerical examples are given using the open-source computer algebra system Yacas, and Yacas is also used sometimes to cut down on the drudgery of symbolic techniques such as partial fractions. Proofs are given for all important results, but are often relegated to the back of the book, and the emphasis is on teaching the techniques of calculus rather than on abstract results.
Students will take a sequence of events or steps for some process and create an algorithm. This could apply to any content area. They will display the algorithm in flowchart form. This activity can be modified for all grade levels and content areas.