The example of two travelers meeting somewhere along the road has been a stereotypical joke about algebra as long as algebra has existed. Here in this detailed presentation, this old trope gets a careful and approachable treatment....

Writing an equation of a line is as easy as m and b. A lesson presentation gives individuals different strategies for writing equations of lines. Some items provide a slope and a point while others provide two points. Whatever the given,...

How many people do you need in a room before two likely share the same birthday? Scholars consider this puzzle by analyzing a set of data. They ponder how to divide the data and determine the proper size of a group for this event to...

Challenge the class to determine whether two quantities are proportional. The second lesson in a unit of 22 has class members decide if two quantities have a proportional relationship. If a proportional relationship exists, the pupils...

Learners determine whether there is a constant multiple within the table through an instructional activity that presents a method for determining whether two quantities are proportional. Pupils analyze tables to determine if they...

Introduce pupils to the two types of reasoning, inductive and deductive. Classmates work in pairs or small groups to learn the difference between the two and apply these reasonings to develop valid conclusions. 

Scholars determine how long it takes to build a birdhouse with the second activity on using equations with proportional relationships. The resource uses examples such as birdhouse building and produce prices to encourage pupils to write...

Work together to find proportional relationships. The sixth portion of the 22-part unit is a collaborative exercise. Teams work with given representations of relationships and determine if they are proportional by creating tables and...

Reflect on altering scale factors. The last lesson in the series of 22 has the class compare the two scale drawings they created. They realize that the scale drawing becomes a scale drawing of each other. Class members continue to work...

The learner puts reasoning and estimation to work. The directions are to place a decimal in the answer to make the equation true. Pupils are to look at the two problems, one multiplication and one division, and estimate an answer. No...

Help your class make sense of quantities and their relationships. Given is the product of two numbers. It is up to your number crunchers to think about the quantitative relationship when the product is one-tenth or ten times the product...

Not all relationships with a pattern are proportional. Show your class why in the fourth installment of a 22-part series. The lesson builds upon previous parts and has pupils analyze tables to determine whether they represent a...

Graphing all kinds of situations in one and two variables is the focus of this detailed unit of daily lessons, teaching notes, and assessments. Learners start with piece-wise functions and work their way through setting up and solving...

An exercise in finding the area of polygons by decomposing into triangles and composing into rectangles is the focus of this resource. Make several copies of the worksheet for each participant. Ask learners to use colored pencils to...

Solving problems about pen and paper with systems of equations ... or is it the other way around? In the lesson, learners first interpret expressions and use equations in two variables to solve problems about notebooks and pens. They...

This turn-key unit on ratios and unit rates walks through a 30-lesson unit on teaching proportional reasoning, with each lesson broken into detailed teaching notes and time allotments for all parts. An unbelievable resource when taken...

Logical thinking is at the forefront of this jam-packed lesson, with young mathematicians not only investigating geometric concepts but also how they "know what they know". Through each activity and worksheet, learners wrestle with...

Use proportions to determine the travel distance in a given amount of time. The 10th installment in a series of 33 uses tables and descriptions to determine a person's constant speed. Using the constant speed, pupils write a linear...

Find the faster rate. The resource tasks the class to compare proportional relationships represented in different ways. Pupils find the slope of the proportional relationships to determine the constant rates. They then analyze the...

Progress from proportional relationships to linear functions. Pupils first review concepts of proportionality covered in earlier grades. They then extend these concepts to linear functions, such as determining the slope of a...

The idea in the resource is to understand the connections between proportional relationships, lines, and linear equations. To stay within the context of the standard, skip the part of the resource that solves with unit rates. Instead,...

Does the explanation make sense? Sample items highlight claim three, communicating reason, in the Smarter Balanced assessments. Teachers use the 16 items to help show pupils the importance of communication and reasoning within...

Explore linear and nonlinear models to help your class build their function skills. In a continuation of the previous lesson, learners continue to analyze and sketch functions that model real-world situations. They progress from linear...

An excellent activity using word problems where pupils interpret and compute quotients of fractions. The commentary includes using a fraction bar model and equations to represent the problem. In this variation of the resource, the...