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There are so many ways to look at definite integrals; What is a fun way to practice? The Gallery Walk on Riemann Sums, Area, and Definite Integrals will offer your students problems converting Riemann Sums to definite integrals, finding area between to curves, Trapezoidal Rule, Left, Right and Midpoint Riemann Sums and determining overestimates and underestimates. What is included:10 “Pictures” with questions.Graph using Left (and Right ( Riemann Sums. Graph using Trapezoidal Rule

What is a meaningful way to relate Riemann Sums to integration? In this introductory lesson on approximating area of an irregular shape, we will explore graphically, numerically (in charts) and algebraically how to determine a Right Riemann Sum and a Left Riemann Sum. Concepts in this lesson are:Riemann Sums solved using a graph.Riemann Sums determined from a function with and without technology.Determining Riemann Sums from a chart with regular intervals and with varying widths. Determining

How do I help my students realize their errors with Separation of Variables?. In this Error Analysis on Differential Equations, students will identify common errors and then rework the problem correctly. These ten problems will give students practice on separation of variables, adding C to one side, exponentiating to solve log problems, and when to consider positive and negative answers. Each problem is on its own separate sheet, but I’ve also included an answer sheet that can hold up to 5 probl

Students need a lot of practice in implicit derivatives for fluency because they tend to make a lot of mistakes. In this Error Analysis on Implicit Differentiation, students will identify common errors and then rework the problem correctly. The twelve problems cover both 1st and 2nd derivatives and writing the tangent line equation. Each problem is on its own separate sheet, but I’ve also included an answer sheet that can hold up to 6 problems. This allows the teacher plenty of flexibility to us

What is a fun way for students to practice integration fluency? In this antiderivative activity sheet, students will solve 16 indefinite integrals, but there are 26 answers to choose from. The distractors are all common mistakes that students make when finding antiderivatives. (Note: This is basic integration with NO substitution problems.) The no prep worksheet has students decode a quotation from a famous mathematician. It’s a fun way for them to self-check their work without just giving them

Optimization, like all word problems, are difficult for students. Students will explore optimization problems using given equations and where they provide the needed geometric formulas to determine the maximum or minimum. The anchor charts provide students with steps for solving for absolute extrema by checking endpoints, and when needed, using the second derivative test. The no prep lesson and worksheet are easy for students to follow and complete. Afterwards they can take the formative assessm

How do my students learn the significance of taking the second derivative? This introduction to determining concavity, inflection points, and using the second derivative test is easy to follow and understand. The anchor charts lead the students into determining concavity and locating inflection points. Using the second derivative test, they will also practice determining if critical numbers are relative extrema. Included in this product:· Lesson on the Second Derivative with examples. · Guide

How do I teach my students how f, f’, and f’’ are related? The Gallery Walk on Applications of Derivatives will give your students practice in analyzing graphs of derivatives analytically, numerically, and graphically. Students will graph f(x) from f’(x), and the reverse. They will read charts of f’ and f’’ to graph f. They will analyze a function by taking its derivatives to graph. Finally, they will differentiate f, f’, and f’’ graphs. All of these require levels 2 through 4 of learning. Man

How do I help my students gain confidence in solving optimization word problems? These task cards offer 8 common types of optimization problems for students to practice. The guide sheet has a nine-step procedure for students to follow when solving these problems. Each task card has a solution card that you and your students may use to aid in discussion of the solutions. Finally, after the students feel confident with these 8 problems they can take the quiz, which mirrors the task cards. What

One of the best ways for students to learn is by correcting mistakes- theirs or someone else’s. The Error Analysis of Derivative Applications will give students an opportunity to find common mistakes when determining tangent lines, critical numbers, extrema, interval of increasing and decreasing, inflection points, and concavity. Students will identify the mistake and then solve the problem correctly. Each problem is on a separate sheet, so you can mix and match to your students’ needs. The sol

Halloween is a great time to review both limits and basic differentiation. Students solve 20 problems, 10 on limits, and 10 of differentiation, then they use the answers to decode the Halloween riddles. This is a great review activity because it covers over 10 AP calculus standards. In the limit questions, Standard CHA-2.B.1 can be used to solve five problems. What’s Included:· 20 problems: 10 limits, 10 differentiations · 3 Halloween riddles to decode using the answers and key. · Answers to a

Do you need a meaningful activity for the holidays? The chain rule activity, “Christmas Chains” helps students develop an understanding of how the chain rule works. The five questions on each worksheet are related, adding an extra composition with each successive question. Many students who have struggled with the chain rule, understand it after this activity. To help decorate your room: Print the worksheets on colored paper. After students complete the worksheet, they can make paper chains wi

How do I get my students to practice more related rates problems? These Halloween themed task cards make learning position, velocity, and acceleration AND related rates more enjoyable. There are 15 problems: the first 4 are PVA and the remaining 11 are Related Rates. Give students all 15 or chose 10 to differentiate according to students’ abilities. Just copy the questions, cut in half, and distribute to students. (Laminate if you choose.) What’s Included:· 4 PVA (Position, Velocity, Accelerati

Students love an excuse to get up and move around the room or out in the halls. The Gallery Walk on Derivatives will give your students more practice in determining rates of change both average and instantaneous. There are several numeric problems using basic derivative formulas as well as estimating a derivative. This can be used for practice or as an assessment. Two types of answer sheets are provided – one to show work and one for just the answers. For the instructor’s convenience, a solutio

Students often have difficulty with piecewise functions. These Task Cards give your calculus students plenty of practice in determining continuity both graphically and analytically. Students may work individually, in pairs or other small groups, or they may complete them as an Easel assignment. Allow about 4 to 8 minutes per card. What is included:· 16 Task Cards o 5 Pairs of Piecewise Functions – one determines continuity graphically, one analytically. o 1 pair of definitions: one lists con

Students love an excuse to get up and move around the room or out in the halls. The Gallery Walk on Limits will give your calculus students practice in determining limits numerically, graphically, analytically, and verbally. There are ten “pictures” in the gallery. Students may use the solution sheet or write the answers in their math notebook. For your convenience, an answer guide to all the problems is provided. Students may work individually, in pairs or other small groups. Allow about 4 to

One of the best ways for students to learn is by correcting mistakes- theirs or someone else’s. The Error Analysis of Derivatives will give students an opportunity to find common mistakes when applying the product rule, quotient rule, and chain rule. Students will identify the mistake, determine what strategy to use, and then solve the problem correctly. Each problem is on a separate sheet, so you can mix and match to your students’ needs. The solution sheet immediately follows your problem s

One of the best ways for students to learn is by correcting mistakes- theirs or someone else’s. The Error Analysis of Limits will give students an opportunity to find common mistakes when taking limits especially for indeterminate forms. Many strategies are covered from substitution to complex fractions. Students will identify the mistake, determine what strategy to use, and then solve the problem correctly. Each problem is on a separate sheet, so you can mix and match to your students needs.

What is VANG? It is the four ways to represent a function- Verbal, Analytical, Numerical, and Graphical. By identifying functions using all these types of expressions, students will demonstrate a deep understanding of the function. This set of cards can be used as a group activity. Each student is given a card that describes a function verbally, analytically, numerically, or graphically, and then they find the other three students with cards that match their function. This activity can

Students often find success with the first derivative test once they understand how to apply it. By working through the examples visually and analytically, then applying the anchor chart, students can determine where the relative extrema are located. This lesson can be used as an introduction to the first derivative test, as remediation, or as review. Concepts included in this lesson are:Determining increasing and decreasing intervals. The First Derivative Test.Relative maximum and minimum