Curated OER
Logic and Proof Writing
Students define inductive and deductive reasoning and write two column proofs. In this geometry lesson, students analyze arguments and draw conclusion. They define steps necessary to arrive at the correct answer when completing proofs.
College Board
2008 AP® Calculus BC Free-Response Questions
The AP® exam is not just about the calculations. By reviewing the free-response questions from 2008, teachers and pupils see that several items require justifications and explanations to gain full credit. The chief reader even points out...
College Board
2009 AP® Calculus AB Free-Response Questions
What was one of the big takeaways from 2009? By reviewing the released AP® Calculus free-response questions, pupils and teachers realize that performing mathematics is not all there is to doing well on the exam. Several items require...
Geometry Accelerated
Accelerated Geometry Review Sheet
Your geometry learners use their knowledge of various geometric concepts to write proofs. Starting with givens containing parallel line segments with transversals and triangles and quadrilaterals, and the mid-point and distance formulas;...
EngageNY
Unknown Angle Proofs—Writing Proofs
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.
Curated OER
Half Math Quilt
Help your third graders become familiar with equivalent fractions for one-half by having them create a quilt. They will use triangles to create a quilt of equivalent fractions over a period of 6 days. As they create the quilt pieces they...
CCSS Math Activities
Smarter Balanced Sample Items: 6th Grade Math – Claim 3
Communication is key. Eight sample items show how important communication and reasoning is for sixth grade mathematics. Part of the Claim 2-4 slide show series, the presentation uses concepts from fifth and sixth grade to illicit...
Curated OER
Measuring Angles
Solve and complete 18 problems about angles. First, demonstrate that each conjecture is false by giving a counterexample. Then write the inverse, contrapositive, and converse for the each statement. In addition, write a...
Inside Mathematics
Graphs (2004)
Show your pupils that perimeter is linear and area is quadratic in nature with a short assessment task that requests learners to connect the graph and equation to a description about perimeter or area. Scholars then provide a...
Mathematics Vision Project
Module 3: Geometric Figures
It's just not enough to know that something is true. Part of a MVP Geometry unit teaches young mathematicians how to write flow proofs and two-column proofs for conjectures involving lines, angles, and triangles.
EngageNY
Unknown Angle Proofs—Proofs with Constructions
Provide your emerging mathematicians with the tools to learn as they incorporate auxiliary lines to solve unknown angle proofs in this continuing segment. They decipher information from a diagram to uncover the missing pieces and...
CCSS Math Activities
Smarter Balanced Sample Items: 7th Grade Math – Claim 3
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...
Curated OER
Fact Families - 6, 7, and 42
Learners investigate the problems that can be solved only using the numbers 6, 7, and 42. They write the correct number sentences and solve for the solution. Students then give a written explanation for how the problem was solved and the...
Curated OER
Justifying Answers
Young scholars study story problems and learn how to find and justify their answers. They will use a story problem and then respond to the prompt questions from the teacher. They must add and subtract facts to 6 and learn how to justify...
Curated OER
Shapely Figures
Students are given magazines, scissors, glue, and one sheet of construction paper. They look for pictures showing real life representations of rectangular prisms, spheres, cones, and pyramids. Pupils cut out pictures showing each of...
Curated OER
New Deck: Percents
Fifth graders observe and demonstrate the meaning of percents by creating a new deck of fifty-two cards. They meet a specified criteria, with a specific percent of the cards being prime numbers, eight's, multiples of five, face cards,...
Curated OER
Around We Go!
Students make accurate measurements and calculations of measuring the area an perimeter of a section of the floor accordingly. They use appropriate measurement and calculation strategies to write a complete a clear explanation for how...
Math Mammoth
Integers
For this integers instructional activity, students solve and complete 4 different types of problems. First, they multiply a positive integer times a negative integer and write as a negative number. Then, students divide a negative...
Curated OER
The Escape
Students find strategies for investigating number problems. They find a common multiple of a group numbers. The teacher introduces the problem and students read and think about it. In groups, students discuss the problem and write...
Inside Mathematics
Quadratic (2006)
Most problems can be solved using more than one method. A learning exercise includes just nine questions but many more ways to solve each. Scholars must graph, solve, and justify quadratic problems.
California Education Partners
Soccer Snacks
Make the cookies healthy. The assessment task asks pupils to determine the number of cookies they could make based on a given amount of ingredients. Given two sugar substitutes, learners determine which substitute would be better and...
Curated OER
Steps and Examples for Multiplying Ratiuonal Expressions
In this multiplying rational expression worksheet, students are given two examples of how to multiply and then simplify rational expressions. The examples are complete with steps and justifications.
Curated OER
Measuring the Classroom
Students measure their classroom and determine the area. They discuss the margin of error. Each class member will write up their results separately. Students must decide what measurements to make, and attempt to measure accurately.
Curated OER
Making Movies
Students use interactive white boards to solve math problems. In this math problems lesson plan, students produce math casts where they can solve problems, write out descriptions, and communicate what they know and do not know on the...