Illustrative Mathematics
Comparing Rational and Irrational Number
Algebra learners must know how to use rational numbers to approximate irrationals. This resource asks participants to decide which number is larger without using a calculator. It makes a great exercise to use as a five-minute transition...
Improving Measurement and Geometry in Elementary Schools
The Sum of the Interior Angles of a Polygon
Junior geometers discover that polygons can be decomposed into triangles and that the number of triangles can be determined by a rule. Note that the Geometer’s Sketchpad® software is required to carry out all components of this...
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Property Lists for Quadrilaterals
Students establish classifications of shapes by various properties (angles, sides, etc.). They introduce the important properties of common shapes. Students develop an awareness of the wide variety of ways the 2-D shapes can be alike.
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Venn Diagram Lesson Plan
Students use Venn diagrams in order to classify different objects and numbers. They then use "Venn Diagram Shape sorter" applets on the computer.
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Space Crossing
Students critically follow a chain of reasoning to devise a decent problem solving technique to be applied to a reasonable problem. They also examine how to use logical arguments.
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Venn Diagram with Blocks
Fifth graders classify blocks according to their attributes. In this math lesson, 5th graders will identify attributes of blocks, sort them, then form the groups into a Venn Diagram, and write ratios using the attributes.
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Getting to the Bottom of the Pyramids
Middle schoolers work together to develop logical arguments about pyramids and chain letters. They share their ideas with other groups and create a diagram showing the breakdown. They discuss the results.
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Adam's Watch
Third graders use their watches to tell the time while the teacher lists their responses on the board along with the reasons for them (set incorrectly, gain/lose time). They solve the problem in pairs and focus their thinking on the...
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Lake Crossing II
Students complete the following problem by using logic: Three couples, the Smiths, the Jones and the Browns wanted to go to the Brown's yacht that was moored a little way out in the lake. There was a dinghy to take them to the yacht but...
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Multiplication Algorithm (1)
Third graders in a 3rd grade math class make connections from prior instruction and mastery to solve problems in new learning situations. Using logical thinking and prior knowledge to solve current math problems is the focus of this...
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Noughts
Students try to figure out the strategies to the game Noughts. Students logic must play a part in the process of the game. Students apply the symmetries of regular polygons. Students devise ways to critically follow a chain of reasoning.
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Circles and Clocks, Shapes and Time
Students work in groups to research clocks and practice telling time. In this telling time lesson plan, students use the computer program ProQuest to study circles, including radius and diameter, and practice drawing circles using a...
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Exam One Review
In this secondary mathematics activity, students solve problems that involve patterns, arithmetic and geometric sequences, geometric logic and reasoning, and changing bases. The three page activity contains fourteen problems. ...
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Mathematical Proofs
High schoolers explore the nature of mathematical proofs and mathematical inquiry. They complete the activity "Using the Pythagorean Theorem". They read selected articles and participate in class discussions.
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Angle Attributes and Measures
Seventh graders explore the concept of angles. In this angles lesson, 7th graders use protractors to measure angles. Students sing an angle song. Students discuss attributes of angles using a two-color plate manipulative.
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Hare and Lynx Population
Fourth graders study changes in animal population. For this graphing lesson, 4th graders create graphs from information read to them about hares and lynx populations. They will describe patterns of change in the graphs and discuss why...
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Mathematical Induction
In this Algebra II worksheet, 11th graders explore two examples of arguments that can be formalized with mathematical induction. The one page worksheet contains two problems with explanation.
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Weighing Time
Pupils devise a strategy to solve problems that is done in a systematic and mathematical fashion. The finding of the unknown value is the focus of the lesson. To solve linear equations proficiently is the skill of the lesson.
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Can Stack
Students are able to find the rule for summing consecutive numbers;
identify the pattern of triangular numbers. They then solve the given problem using logic and mathematical reasoning.
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Time Problems
High schoolers make sensible estimates and check for reasonable results. They also solve problems with positive and negative integers using practical activities or models as needed.
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Make the Highest Total
Sixth graders predict the outcome of a simple probability experiment, test it and explain the result by using problem solving strategies to explore situations mathematically. They then play a few games informally where students play in...
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Brian's Pegboard I
Third graders focus on developing a systematic approach to problem solving while working on a problem that requires them to determine possible outcomes. They use a pegboard as a manipulative in this problem.
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Analysis of Atmospheric Conditions for a High Mountain Retreat
Students examine the relationship between altitude, atmospheric pressure, temperature and humidity at a particular location. They practice science and math in real world applications. They write reports detailing their scientific...
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Looking into Eratosthenes' Radius of the Earth
Students, in small groups, research Eratosthenes and his calculations of the Earth's radius. They write a summary of the person, the experiments and his calculations to determine how accurate Eratosthenes was in his estimations of the...