## All Lessons ### Don't Freeze the Engine

9-12
In this lesson, students will learn to read an antifreeze chart to determine the necessary mix of antifreeze and water for protection against various temperatures. Students will then numerically analyze a particular cooling system to determine how much fluid to drain in order to get the desired percent concentration of antifreeze. Finally, students will set up a system of equations to solve the same system. ### Do You Notice Sum-Thing?

6-8, 9-12
This lesson invites students to investigate the patterns when a "plus sign" (a cross-shaped arrangement of five squares) is placed on the board in various locations. Students will conjecture about the pattern of the five displayed numbers, the sum of the five numbers, and any other patterns that they notice. Students may also explore similar patterns when other shapes, such as a 2 × 1 rectangle, are placed on the hundreds board. ### Analyzing Numeric and Geometric Patterns of Paper Pool

6-8
This mathematics excursion is based on the Paper Pool Project from the Comparing and Scaling unit of the Connected Mathematics Project, G. Lappan, J. Fey, W Fitzgerald, S. Friel and E. Phillips, Dale Seymour Publications, (1998), Paper Pool Project, pp.106-111. 3-5
This lesson focuses on forming 3-digit address numbers to meet specific requirements. Careful reading of information and understanding of mathematical language are important to finding appropriate solutions. Using the problem-solving strategies of looking for patterns and establishing an organized list will aid students in finding all the possible solution sets. ### Analyzing the Data

9-12

In the third lesson, students identify a function that models the data. An interactive graphing tool can be used to determine a function that fits the data points. 6-8
This lesson focuses on forming numbers which meet specific requirements. Careful reading of information and understanding of mathematical language are important to finding appropriate solutions. Using the problem-solving strategies of looking for patterns and establishing an organized list will aid students in finding all the possible solution sets. 6-8
In the following grades 6-8 lesson, students participate in activities in which they focus on the uses of numbers. The activities explore how students use numbers in school and every day settings as a way for students and the teacher to get to know each other at the beginning of the school year. ### Elapsed Time: Using a Timeline to Determine Elapsed Time

3-5
Students learn to calculate elapsed time by using a timeline, and then complete three engaging and fun activities that plan a circus performance, their class schedule, and their day. ### Gerrymandering: Is It or Isn't It?

9-12
Congressional districts are redrawn after a census year (conducted by the federal government every 10 years) to reflect shifting populations. Political scientists say there is a major advantage for whichever political party has control of a state legislature when districts are redrawn. However, during the process, the minority party tends to make accusations that districts are being gerrymandered, or drawn in unnatural ways to manipulate voter populations that would favor the majority. In this lesson, students explore how mathematics can be used to make decisions about whether a given congressional district is or is not being gerrymandered. They also use objective measurements to explore the ambiguity that is inherent in the process. ### Bean Salad: Using Algebraic Reasoning to Determine Quantities of Ingredients

3-5
In this lesson, students use operations of whole numbers and/or fractions to determine the precise numbers of three types of dried beans needed to make salads. The use of manipulatives and partner activities provide differentiation and support learning for students of varying abilities. ### Egg Carton Designs: Constructing Arrays to Begin a Study of Multiplication

3-5
In this lesson, students are presented with a design challenge: a company that produces egg cartons wants to create a package for 24 eggs. The company wants to know all of the possible ways to arrange 24 eggs into rectangular packages. Students work together to find the arrays and respond to the egg company. ### A Ratio that Glitters: Exploring the Golden Rectangle

6-8, 9-12
In this lesson, students will develop an understanding of the Fibonacci Sequence (and its connection to Golden Rectangles), Golden Ratio, Golden Rectangle, and the term ratio (as it applies to rectangles). Students will use tools and construction techniques to demonstrate geometry prowess and be able to observe the Golden Rectangle in nature and in the classroom. ### Folding Circles: Exploring Circle Theorems through Paper Folding

9-12
In this lesson, students will manipulate three paper circles to explore four circle theorems. Using paper folding allows the lesson to be more accessible to kinesthetic learners. ### Getting the (Decimal) Point with Blocks: Multiplying Two Decimals Using Base Ten Blocks

3-5
Students will use base ten blocks to model decimal multiplication. They will assign different values to the different base ten blocks to explore the consistent relationship between the types of blocks. They will also discover different factors for the same product. These activities will help students develop a conceptual understanding of decimal multiplication. ### Coin Blocks: Counting Money with Value-Sized Blocks

Pre-K-2
Students use coin blocks, a concrete representation of coins, to compose and decompose numbers by counting money. They also use an interactive tool to practice the same skills pictorially. ### Basically Base Ten: Discovering Place Value Meaning Using Base Ten Blocks

Pre-K-2
In this lesson, students use base ten blocks to construct two- and three-digit numbers on a place value board. They then play a game using base ten blocks to model numbers up to 100. ### A Squadron of Bugs: Introducing Division with Remainders with a Book

3-5
This hands-on lesson uses the book, A Remainder of One, by Elinor J. Pinczes, to introduce division with remainder. Students will enjoy the story context as they explore different remainder situations and model division with arrays. ### DiRT Dash: Planning the Fastest Route across Various Terrains

6-8
The shortest distance between two points is a line. But what is the shortest time to travel between two points on different terrains? In this lesson, students will predict, estimate and then calculate the path that results in the fastest time to travel between two points when different terrains affect the fastest path. This lesson is designed as an introduction to the Calculation Nation® game DiRT Dash and prepares students to apply mathematics to improve their performance in the game. ### Fraction Feud: Comparing and Ordering Fractions

3-5
In this lesson, students use fraction bars to explore how to compare sizes of fractions. They conclude with an online Calculation Nation® game called Fraction Feud. ### Chocolate FACTORy: Finding Factors of Numbers 1 Through 36

3-5
In this lesson students create rectangular arrays to represent sizes of chocolate boxes. They find all of the factors of each number up to 36 and learn the difference between prime and composite numbers. Then they play an online game to practice finding factors for each product up to 36.