Students build scale models of objects of their choice. In class they measure the original object and pick a scale, deciding either to scale it up or scale it down. Then they create the models at home. Students give two presentations along the way, one after their calculations are done, and another after the models are completed. They learn how engineers use scale models in their designs of structures, products and systems. Two student worksheets as well as rubrics for project and presentation expectations and grading are provided.

The purpose of this course is to expose you to the wider world of mathematical thinking. There are two reasons for this. First, for you to understand the power of quantitative thinking and the power of numbers in solving and dealing with real world scenarios. Secondly, for you to understand that there is more to mathematics then expressions and equations. The core course is a complete, ready to run, fully online course, featuring 9 topics: Problem solving, voting theory, graph theory, growth models, consumer finance, collecting data, describing data, probability, and historical counting. Additional optional topics are provided. The course materials can easily be used with a face-to-face course.

Students use the Hot Air Balloon simulation to model integer subtraction. They then move to modeling subtraction on a number line. They use patterns in their work and their answers to write a rule for subtracting integers.Key ConceptsThis lesson introduces the number line model for subtracting integers. To subtract on a number line, start at 0. Move to the location of the first number (the minuend). Then, move in the negative direction (down or left) to subtract a positive integer or in the positive direction (up or right) to subtract a negative integer. In other words, to subtract a number, move in the opposite direction than you would if you were adding it.The Hot Air Balloon simulation can help students see why subtracting a number is the same as adding the opposite:Subtracting a positive number means removing heat from air, which causes the balloon to go down, in the negative direction.Subtracting a negative number means removing weight, which causes the balloon to go up, in the positive direction.The rule for integer subtraction (which extends to addition of rational numbers) is easiest to state in terms of addition: to subtract a number, add its opposite. For example, 5 – 2 = 5 + (–2) = 3 and 5 – (–2) = 5 + 2 = 7.Goals and Learning ObjectivesModel integer subtraction on a number line.Write a rule for subtracting integers.

Every month we will give you a math/statistics brain teaser that lets you test your knowledge with a fun problem.Many of the ideas in these Teasers come from thoughts formed by some of the great mathematical/statistical geniuses in history.

Philanthropy is a core value of Native American tribes in Oregon. Many tribes refer to this as the “spirit of potlatch,” which is a tradition that goes back hundreds and possibly thousands of years. In this spirit, many tribes have created charitable foundations or funds to support causes that benefit the local and surrounding communities. Collectively, tribal foundations are among the largest sources of philanthropy in Oregon.This lesson uses the mathematical practice of fractions to introduce students to Native philanthropy. Students are given a dataset and asked to perform fraction concepts and justify their choices as part of a philanthropic effort. Students will be addressing Critical Areas 1 and 2 while addressing mathematical practices.

Lesson OverviewStudents solve a classic puzzle about finding a counterfeit coin. The puzzle introduces students to the idea of a scale being balanced when the weight of the objects on both sides is the same and the scale being unbalanced when the objects on one side do not weigh the same as the objects on the other side.Key ConceptsThe concept of an inequality statement can be modeled using an unbalanced scale. The context—weighing a set of coins in order to identify the one coin that weighs less than the others—allows students to manipulate the weight on either side of the scale. In doing so, they are focused on the relationship between two weights—two quantities—and whether or not they are equal.Goals and Learning ObjectivesExplore a balance scale as a model for an equation or an inequality.Introduce formal meanings of equality and inequality.

This course is an introduction to problem solving; logic, sets, and operations on sets; and properties and operations on whole numbers, integers, rational numbers, irrational numbers, and real numbers. Modelling techniques necessary for future elementary educators will also be covered in this course.

This problem introduces a logistic growth model in the concrete setting of estimating the population of the U.S. The model gives a surprisingly accurate estimate and this should be contrasted with linear and exponential models, studied in ``U.S. Population 1790-1860.'' This task requires students to interpret data presented.

This resource provides students with the opportunity to solve a multi-step contextual word problem with a degree of difficulty appropriate to Grade 4, requiring application of knowledge and skills.

A+ Click is an interactive collection of more than 3700 math problems and answers for K-1 K-12 school program. It defines the personal level of math knowledge. You move up into the next level if you give 5 correct answers in a row. Practice makes perfect.

This is a rigorous, open, and equitable Calculus I class. It follows the OpenStax Calculus I book and uses the MyOpenMath course created by Larry Green and the ZTC grant as homework and extra resources. As well as lecture notes and worksheets created in Microsoft Word.

The structure of the course is that it follows a flipped class model, where students are required to watch lecture video created off of the lecture notes. Then students work on sectional exercises embedded in Canvas from MyOpenMath and work by themselves on the hard worksheet before the last day of the class during the week. On that day of class students will have the opportunity to work in groups on the worksheet problems.

They will be motivated to work on the problems in their groups because they will then teach the professor their random problem received as well as their group mates have points associated with their group mates work. The way they do this is through a program called GoReact that is embedded in Canvas. The main thing about this program is that students can easily share a recorded video of them teaching the math to the professor and the professor in turn can give video feedback telling the student how much they rock or letting them know what went wrong. These Teach Me Video are the foundation of the course and are the only thing the professor grades for the week unless there is a test. They are fun for both the instructor and students and increase the teacher student relationship as well as the student to student relationship. It is also easy to bump the Teach Me Videos up to make students who didn't fully understand the problem by making them redo the video to get some points back.

Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying algebraic expressions. Use the game screen to test your multiplication and factoring skills!

This Remote Learning Plan was created by Julie Rankin in collaboration with Craig Hicks and Tyler Cronin as part of the 2020 ESU-NDE Remote Learning Plan Project. Educators worked with coaches to create Remote Learning Plans as a result of the COVID-19 pandemic.The attached Remote Learning Plan is designed for 5th grade math students. Students will learn how to multiply fractions with models. This Remote Learning Plan addresses the following NDE Standard: MA5.1.2.c It is expected that this Remote Learning Plan will take students 45 minutes to complete. Here is the direct link to the Google Doc: Multiply Fractions with Models 

Students use the Hot Air Balloon interactive to model integer addition. They then move to modeling addition on horizontal number lines. They look for patterns in their work and their answers to understand general addition methods.Key ConceptsTo add two numbers on a number line, start at 0. Move to the first addend. Then, move in the positive direction (up or right) to add a positive integer or in the negative direction (down or left) to add a negative integer.Here is −6 + 4 on a number line: The rule for integer addition (which extends to addition of rational numbers) is easiest to state if it is broken into two cases:If both addends have the same sign, add their absolute values and give the result the same sign as the addends. For example, to find −5 + (−9), first find |−5|  +|−9| = 14. Because both addends are negative the result is negative. So, −5 + (−9) = −14.If the addends have different signs, subtract the lesser absolute value from the greater absolute value. Give the answer the same sign as the addend with the greater absolute value. For example, to find 5 + (−9), find |−9| − |5| = 9 − 5 = 4. Because −9 has the greater absolute value, the result is negative. So, 5 + (−9) = −4.Goals and Learning ObjectivesModel integer addition on a number line.Learn general methods for adding integers.

Build rectangles of various sizes and relate multiplication to area. Partition a rectangle into two areas to discover the distributive property.

Putting Math to Work

Type of Unit: Problem Solving

Prior Knowledge

Students should be able to:

Solve problems with rational numbers using all four operations.
Write ratios and rates.
Use a rate table to solve problems.
Write and solve proportions.
Use multiple representations (e.g., tables, graphs, and equations) to display data.
Identify the variables in a problem situation (i.e., dependent and independent variables).
Write formulas to show the relationship between two variables, and use these formulas to solve for a problem situation.
Draw and interpret graphs that show the relationship between two variables.
Describe graphs that show proportional relationships, and use these graphs to make predictions.
Interpret word problems, and organize information.
Graph in all quadrants of the coordinate plane.

Lesson Flow

As a class, students use problem-solving steps to work through a problem about lightning. In the next lesson, they use the same problem-solving steps to solve a similar problem about lightning. The lightning problems use both rational numbers and rates. Students then choose a topic for a math project. Next, they solve two problems about gummy bears using the problem-solving steps. They then have 3 days of Gallery problems to test their problem-solving skills solo or with a partner. Encourage students to work on at least one problem individually so they can better prepare for a testing situation. The unit ends with project presentations and a short unit test.