Fourth graders design a table and chair arrangement. In this mathematical reasoning lesson, 4th graders place tables shaped like equilateral triangles so that they seat the appropriate number of guests. 

Can your classes apply the knowledge they have learned? Use this performance task to find out! Individuals use transformations to explain congruence and angle relationships within parallel lines to find missing values. They show what...

This a fun problem for young geometers to play with while gaining important insight into deductive reasoning. Some will find the answers very quickly, others might take a less direct path, but all will use their knowledge of the sum of...

In critiquing someone else's theory, learners share insight into their own understanding of mathematical concepts. Fifth graders will explore the notion that products are always larger than their factors. While this statement is...

It turns out math IS for the birds! Here, learners use mathematical reasoning to determine how often someone needs to fill a bird feeder. The rate the feeder empties varies by the number of holes that are available to the birds. Day two...

Students reason mathematically as they solve problems dealing with probability of an even occurring. In this probability lesson, students differentiate between different rankings of candidates running for leadership. They identify...

Students differentiate between inductive and deductive reasoning. In this geometry instructional activity, students identify congruent figures and examine logos for congruency.

In this real-world problem about the rapid growth of rabbit populations, students must analyze two different scenarios and create mathematical models to represent them. They use their exponential models to answer questions about the...

What do Sherlock Holmes and geometry have in common? Why, it is a matter of deductive reasoning as the class learns how to justify each step of a problem. Pupils then present a known fact to ensure that their decision is correct.

Playing with mathematics can invoke curiosity and excitement. As pupils construct triangles with given criteria, they determine the necessary requirements to support similarity. After determining the criteria, they practice...

Four simple equations, each with two variables, try to get at the important question of reasoning about equations. The problem isn't to solve the equations, but to understand the nature of their solutions. These equations address the...

Connect your pupils to the problem by presenting a situation with which they can identify. Individuals analyze a graph of water use at a school by reasoning and making conclusions about the day. The instructional activity...

This collaborative activity investigates the meaning of a trapezoid and a parallelogram. It begins by presenting two different definitions of a trapezoid. Learners are to reason abstractly the difference between the two definitions and...

Eighth graders read a book "Counting on Frank" with a partner. Using the text, they identify eight clues and use their mathematical reasoning in real-life situations. They participate in a game and turn in a notebook in which they write...

Show your classes the importance of mathematics in something as simple as bicycle design. The final lesson in the six-part STEM series has each group research a different aspect of the bicycle. Learners use mathematical formulas, linear...

Your young learners will enjoy mathematics that is meaningful correspondence as they play their way to a deep mathematical foundation. Organized around the math standards, this appropriate sequence of conceptual, preschool...

Four is the perfect number—if you're talking about parallelograms. Scholars determine a possible fourth vertex of a parallelogram in the coordinate plane given the coordinates of three vertices. They read a conversation...

Jim and Jesse started their road trip with the same amount of money. Your class must find the amount of money each one had given, the amount of money spent, and the ratio of money at the end. This is a comprehensive problem that...

Keep your pets slim, trim, and healthy using mathematics! Pupils use a linear programming model to optimize the amount and type of food to provide to a pet rabbit. They model constraints by graphing inequalities and use them to analyze a...

Get your learners to think outside the box. Students require a good understanding of ratios and their relationship to fractions to complete the problem. The only quantities given in the problem are the ratio of the number of votes for...

Here is another opportunity for math students to apply reasoning to solve real-world problems with ratios. The ratio of the number of votes for two candidates is provided. Your class is asked to use this ratio and information given about...

Good advertisers can make mathematics seem irrelevant. Teach your classes to use math to see through these tactics and make good decisions. The posed task has pupils analyze sweepstakes statistics to determine and compare the cost of...

This is an opportunity for young mathematicians to apply reasoning to solve real-world problems with ratios. Even though there are three candidates for class president, students will only consider two at a time, making the first problem...

Investigate the proportional relationships of length, area, and volume. Learners use the dimensions of rectangular prisms to create ratios and proportions. They compare the different ratios to solve more advanced problems.