Manchester University
Lesson 51: Scientific Notation
Discuss scientific notation with this mathematics lesson. Middle schoolers predict which problem is bigger of two numbers. They analyze the problems by observing the powers of 10 in order to decide which is bigger. This appears to be an...
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Count on Me
Fourth graders use inductive reasoning to find algebraic patterns in geometric figures. They use technology (i.e., calculators, computers) and manipulatives to discover number patterns involving geometric concepts. They solve concrete...
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What Is A Number?
Seventh graders engage in a lesson that is focused upon teaching the concept of integer numbers with a focus upon the integers. They practice solving different problems using positive and negative numbers. They then attempt to describe...
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Worksheet Chapter 1 College Prep Algebra
In this algebra worksheet, students compare integers, translate words to a numerical expression, identify sets of numbers, identify properties, use order of operations, multiply fractions, and solve simple word problems. This 13 page...
Illustrative Mathematics
Firefighter Allocation
Creating equations with one variable to solve real-world-type problems is a key skill any algebra learner needs to master. Here the focus is on realizing that one can write the equation in different ways depending upon how one...
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Multiplying Polynomials
Students explore multiplying polynomials. They observe solving polynomials using the standard order of operations, FOIL, and the box method. Throughout the demonstration, students explore strategies of solving word problems such as...
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Inductive and Deductive Reasoning
Students use logical arguments and inductive reasoning to make or disprove conjectures. After observing a teacher led demonstration, students discover that the deductive process narrows facts to a few possible conclusions. In groups,...
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The Quadratic Formula 1
In this quadratic formula worksheet, 9th graders identify integers and their proper placement in the quadratic equation. Afterward, they write the new equation in the quadratic formula form and solve. Students complete six quadratic...
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Rational Equations
For this algebra worksheet, students find the common denominator for 8 problems so they can solve for x. The rational equations include binomial expressions as denominators for 5 of the problems.
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Geometric Applications
In this geometry worksheet, students solve 5 word problems. Each of the problems involves finding one side of a right triangle. Story problems relate the Pythagorean Theorem to building ramps, shadows, and the length of a banner.
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Quadratic Equations
In this algebra worksheet, students solve 11 quadratic equations for the given variable. Four problems require students to multiply two binomials. The final 5 problems students are to solve by completing the square.
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Multiplying by 10, by 100, and by 1,000
Fourth graders write tenths and hundredths in decimal and fraction notations. In this math instructional activity, learners know the fraction and decimal equivalents for halves and fourths. Everyone answers numerous questions posed by...
Illustrative Mathematics
Log Ride
The rides at a theme park always have limits on weight or number of riders. This makes a natural example of the use of inequalities to solve real-world problems. Learners explore intuitive solutions using substitution to solve the...
Illustrative Mathematics
How Many Solutions?
Determining the number of solutions is an important stepping stone to higher math. In this case, the resource asks algebra pupils to find a second linear equation for a certain solution of a system. When one is asked for a linear...
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Ratios: Interpreting the Phrase "Out Of"
Students explore the concept of ratios. They observe a website of Trident Gum that gives a real life example of ratios. Students practice ratio problems in three forms. They express ratios as a proportion and solve proportions using...
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Products, Multiples, Factors
In this products, multiples, and factors worksheet, students complete various activities where they solve problems for products, multiples, and factors of numbers. Students complete 14 problems.
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The Complex Numbers
In this algebra worksheet, students solve 16 problems involving imaginary numbers. In the first three, students find the square root of 3 negative numbers in terms of i. Nine problems involve addition, subtraction, multiplication and...
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Patterns and Algebraic Expressions
Scholars will solve problems, create patterns, and write algebraic expressions. In addition, they will learn how to represent a number with a variable.
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Connecting Formulas Related to Geometric Figures
Students identify diagrams of quadrilaterals and circles by different names and classify the figures. They name the areas for each diagram and practice solving the formulas for each.
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Shadow Casting
Eighth graders use a meter stick that is placed on a horizontal surface and an object is moved along it so that the shadow length can be measured at different distances from the light source. They solve real-world problems involving...
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Addition & Multiplication of Matrices
Students add and multiply matrices. They explore the dimensions of products of a matrix. After observing problems on the overhead, students solve their own matrix problems. They list and define the properties of matrix multiplication.
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Formulas, Applications, and Variation
In this algebra worksheet, students solve 7 given formulas for a specified variable. Each formula is written as an equation, and students isolate one of the variables as the solution to the problem.
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The Quadratic Formula
In this algebra worksheet, students solve 10 equations using the quadratic formula. In problems 5, 6, 9 and 10 students must first get the equation in standard form.
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Formulas for Volume and Surface Area
Students calculate the volume and surface area of each shape. In this geometry lesson, students use nets and other three dimensional polygons to create visuals of the volume of a shape. They define important vocabulary words...