Definition: If the quotient of two nonzero real numbers are being raised to an exponent, you can distribute the exponent to each individual factor and divide individually. It was published by Cengage in 2011. Instead of re-teaching the rules that they have all seen before (and since forgotten), I just handed each student an exponent rules summary sheet, this exponent rules match-up activity, and a set of ABCDE cards printed on colored cardstock. RULE 3: Product Property. I have linked to a similar activity for more basic exponent rules at the end of this post! Example: RULE 2: Negative Property. If you are teaching younger students or teaching exponent rules for the first time, the book also has a match-up activity on basic exponent rules. This gave me a chance to get a feel for how well the class understood that type of question before I worked out the question on my Wacom tablet. We can read this as 2 to the fourth power or 2 to the power of 4. Simplify the expression: Open parenthesis begin fraction 2x cubed over 3y end fraction close parenthesis to the power of 4. I think my students benefited much more from it as well. I enjoyed this much more than a boring re-teaching of exponent rules.
For each rule, we'll give you the name of the rule, a definition of the rule, and a real example of how the rule will be applied. This is called the "Match Up on Tricky Exponent Rules. " Student confidence grew with each question we worked through, and soon some students began working ahead. I ran across this exponent rules match-up activity in the Algebra Activities Instructor's Resource Binder from Maria Andersen. Line 3: Apply exponents and use the Power Property to simplify. They are intentionally designed to look very similar. I thought it would make the perfect review activity for exponent rules for my Algebra 2 students. Simplify the exponents: p cubed q to the power of 0. If you have trouble, check out the information in the module for help. Begin fraction: 1 over y to the 6, end fraction. Tips, Instructions, & More are included. I did find a copy of the activity uploaded online (page 7 of this pdf). Students are given a grid of 20 exponent rule problems. See below what is included and feel free to view the preview file.
Begin fraction: 16 x to the power of 12 over 81 y to the power of 4, end fraction. Subtract the exponents to simplify. Begin Fraction: Open parenthesis y to the 2 times 3 end superscript close parenthesis open parenthesis y to the 2 times 4 end superscript close parenthesis over y to the 5 times 4 end superscript end fraction. In this article, we'll review 7 KEY Rules for Exponents along with an example of each. After about a minute had passed, I had each student hold up the letter that corresponded to the answer they had gotten. Exponent rules are one of those strange topics that I need to cover in Algebra 2 that aren't actually in the Algebra 2 standards because it is assumed that students mastered them when they were covered in the 8th grade standards. Click on the titles below to view each example. Write negative exponents as positive for final answer. Each of the expressions evaluates to one of 5 options (one of the options is none of these).
Next time you're faced with a challenging exponent question, keep these rules in mind and you'll be sure to succeed! This resource binder has many more match-up activities in it for other topics that I look forward to using with students in the future. Raise the numerator and a denominator to the power of 4 using the quotient to a power property. If they were confused, they could reference the exponent rules sheet I had given them. Though this was meant to be used as a worksheet, I decided to change things up a bit and make it a whole-class activity. Simplify the expression: open parenthesis p to the power of 9 q to the power of negative two close parenthesis open parenthesis p to the power of negative six q squared close parenthesis. I reminded them that they had worked with exponent rules previously in 8th grade, and I wanted to see what they remembered.
Use the zero exponent property: p cubed times 1. Use the product property and add the exponents of the same bases: p to the power of 6 plus negative 9 end superscript q to the power of negative 2 plus 2 end superscript. For example, we can write 2∙2∙2∙2 in exponential notation as 2 to the power of 4, where 2 is the base and 4 is the exponent (or power). An exponent, also known as a power, indicates repeated multiplication of the same quantity. Plus, they were able to immediately take what they had learned on one problem and apply it to the next. Try this activity to test your skills. Perfect for teaching & reviewing the laws and operations of Exponents. This module will review the properties of exponents that can be used to simplify expressions containing exponents. We discussed common pitfalls along the way. These worksheets are perfect to teach, review, or reinforce Exponent skills! I have never used it with students, but you can take a look at it on page 16 of this PDF.
These are all helpful when connecting to the DPM. Lesson 4: Triangles. Lesson 6: Combining and Separating Shapes.
A square with side length 1 unit, called "a unit square, " is said to have "one square unit" of area, and can be used to measure area. Recently, I added a new addition to the DPM resources: The Distributive Property of Multiplication on Google Slides®. Additional practice 1-3 arrays and properties of solution. So, I'd pose a question? A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. Lesson 5: Area and the Distributive Property.
Relate area to the operations of multiplication and addition. Represent and solve problems involving multiplication and division. All rights reserved. With manipulatives because they make the concept real. What is the Answer, Then? Compare two fractions with the same numerator or the same denominator by reasoning about their size. Where could you break apart the array to make it easier to find the total? Lesson 1: Lines and Line Segments. Which part or parts of the Distributive Property of Multiplication (DPM) do students have difficulty comprehending or learning? Lesson 3: Greater Numbers. They naturally conclude that you would have to ADD both products to get the final product! Additional practice 1-3 arrays and properties misc. Lesson 7: Making New Shapes. Lesson 5: Writing to Explain.
Recognize and generate simple equivalent fractions, (e. g., 1/2 = 2/4, 4/6 = 2/3). Lesson 9: Draw a Picture. It involves notation they are usually unfamiliar with or rarely use: mixed operations and parentheses in the same number sentence. But as teachers know, the pacing guide doesn't wait for you, so I have to keep going to stay on track and meet district guidelines for assessment. Don't rush to teach the Distributive Property of Multiplication number sentences on the first day! Additional practice 1-3 arrays and properties of addition. Multiplication and division facts up to 10: true or false? By the end of Grade 3, know from memory all products of two one-digit numbers.
Solve using properties of multiplication ( 3-N. 9). Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. From there, it was time for independent practice. Lesson 5: Finding Equivalent Fractions. On whiteboards or paper, students practice writing multiplication sentences for the broken-apart arrays. Lesson 1: Multiplication as Repeated Addition. Sometimes I use Direct Instruction. One thing I do with students is practice breaking apart arrays at strategic points. Lesson 6: Use Objects and Draw a Picture. Part 1 and Part 2 each have a Reflection slide at the end for student reflection on what was learned. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Lesson 5: Try, Check, and Revise.
Lesson 7: Two-Question Problems. Lesson 6: Making Sense of Multiplication and Division Equations. All the slides provide more instructions and information to the student in the SPEAKER NOTES section of each slide (similar to the Presenter's Notes area in PowerPoint). Did you ever think that as a third-grade teacher or even an elementary teacher, you would be teaching the Distributive Property of Multiplication? Game Night Seating Plan (optional). We practiced this several times and named the two new arrays with multiplication sentences. 1 Understand that shapes in different categories (e. g., rhombuses, rectangles, and others) may share attributes (e. g., having four sides), and that the shared attributes can define a larger category (e. g., quadrilaterals). Lesson 6: Comparing Numbers. Chapter 10: Fraction Comparison and Equivalence|. Lesson 1: Division as Sharing. I would pick at least three students to share how they broke apart the arrays. Lesson 3: Units of Mass. Lesson 3: Perimeter of Common Shapes. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).
Division facts for 6, 7, 8, and 9: true or false? The DPM center is also great for small groups for those students who are still not getting it or need more practice understanding the process of breaking apart and adding, matching multiplication sentences, or writing DPM sentences. Lesson 5: Making Bar Graphs. English with Spanish Prompts. The first lessons on teaching the Distributive Property must focus on conceptual understanding. Why Is This Important to Know? On day two, I reviewed what we had learned the day before. Then let them follow all the steps in a guided practice problem. We started with a quick warmup with an anchor chart partially prepared. Here are some more highlights about this digital interactive notebook for the Distributive Property of Multiplication. Lesson 1: Representing Numbers.
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). The students could NOT understand why the array was broken apart or what we were adding. We would share ideas, solutions, etc. Which Parts of the Distributive Property of Multiplication Present the Most Difficulties?
On the printable, I have these four steps: - draw a vertical line to split the array. Represent and solve multiplication problems involving arrays. Lesson 5: Work Backward. Lesson 4: Elapsed Time. Interpret whole-number quotients of whole numbers, e. g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. Lesson 4: 6 and 7 as Factors.