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A set of 5 lesson plans based on the Arizona state standards for fourth grade alegbra and patterns.
Algebra and Patterns 1 Running head: ALGEBRA AND PATTERNS: AN INTEGRATED UNIT Fourth Grade Algebra and Patterns: An Integrated Unit Benjamin Sullens University of Phoenix Algebra and Patterns 2 Table of Contents Unit Overview ................................................................................................................... 3 Integrated Unit Matrix ....................................................................................................... 4 Lesson Plans.................................................................................................................... 6 Find the Missing Term .................................................................................................. 7 Writing an Expression................................................................................................. 10 Solving Equations ....................................................................................................... 14 Writing Equations for Word Problems ........................................................................ 18 Change in Quantity ..................................................................................................... 21 Worksheets and Materials for Lessons .......................................................................... 25 Find the Missing Term Day 1 - Worksheet ................................................................. 26 Find the Missing Term Day 2 - Worksheet ................................................................. 27 Find the Missing Term - Number Tiles (Example) ...................................................... 28 Writing an Expression - Worksheet ............................................................................ 29 Solving the Equation - Worksheet .............................................................................. 30 Writing Equations for Word Problems - Worksheet .................................................... 34 Change in Quantity - Worksheet ................................................................................ 36 Assessments and Rubrics.............................................................................................. 40 Solving Equations Quiz .............................................................................................. 41 Algebra & Patterns Post Test ..................................................................................... 42 Oral Presentation Rubric: Water Droplets (Change in Quantity) ................................ 44 References ..................................................................................................................... 45 Algebra and Patterns 3 Unit Overview Unit Title: Algebra, Patterns and Functions Unit Focus: Fourth grade algebra, patterns and functions Unit Length: 10 to 14 days Unit Goals: • Increase students knowledge of Algebraic concepts • Build students confidence when using manipulatives in mathematics • Foster a positive spirit towards mathematics and its usefulness in daily life. Algebra and Patterns 4 Integrated Unit Matrix Science Social Studies Reading Art Discuss how Review important Read the Identify how binary code is dates in history book, Best of numbers (the used in and the time Times by actual shape of Numbers and operations technology. between those Gregory Tang the numbers dates. themselves) are used in art. Discuss Compare Read the book Break down patterns that populations Equal Impressionist occur in nature. based given food Shmequal by paintings and (i.e. colored sources in a given Virginia L. how their use of Algebra rings of a king areas (farming, Kroll patterns affects snake.) fishing, etc.) the paintings as a whole. Analyze Discuss the use Explore the Appraise how symmetry in of patterns in book Chasing shapes and nature. (i.e. ancient Greek Vermee by pattern is used butterfly wings) columns/buildings Blue Balliett by artists to Geometry create masterpieces. (i.e. Piet Mondrain) Algebra and Patterns 5 Interpret the Discuss distances Read the Discuss the growth of plants traveled by book, dimensions of and animals explorers to get to Spaghetti & paintings in an during their life new lands. (i.e. Meatballs for art gallery. Measurement cycle. Columbus, Lewis All! A & Clark) Mathematical Story, by Marilyn Burns Discuss the Review graphs Explore the Discuss the change of a about crop book prices that child having a production in the Araminta's paintings have Data Analysis and certain eye or students state. Paint Box by sold for graph Probability hair color. Karen possible trends. Ackerman Algebra and Patterns 6 Lesson Plans Algebra and Patterns 7 Find the Missing Term Content Standard and/or English Language Development Standard: Math Strand 3 Concept 1 P.O. 1 Level/Grade: 4 Content Objective: TSW find missing terms in a one-step pattern on a worksheet with 8 out of 10 problems correct. Assessment: Completed worksheet Pacing: 2 class periods Target Vocabulary/Primary Language Support: rule, pattern Materials: number cards, worksheets, pencil, smartboard or projector Bloom’s Taxonomy: Remembering Understanding Applying Analyzing Evaluating Creating Multiple Intelligences: Verbal-Linguistic Math-logical Spatial Musical Bodily-Kinesthetic Interpersonal Intrapersonal Naturalist Steps Content Day 1 - Entrance ticket: The teacher will display a (shape) pattern on a smart board/overhead and ask the students to continue the pattern. Discuss with the student what they notice about the pattern. Introduction Day 2 - Entrance ticket: The teacher will give the students a pattern and they must complete it and provide a rule for it. Day 1 - Introduce the lesson vocabulary. Have the student jot down the Input Algebra and Patterns 8 definitions in their math journals. The teacher will introduce patterns in numbers by exploring numbers on a number line (overhead/smart board) Day 2 - This is a reteach/refresher day. The pacing of day 2 depends on student needs. The teacher may wish to do the day 2 activities in small groups. Day 1 - The teacher use number cards that can be used to create a mathematical pattern. The teacher and the student will build a pattern with the manipulatives. The teacher will then ask the students to Guided observe any patterns they notice (ex. add 2, subtract 4, etc.). Practice Day 2 - Using the number tiles, the students will work in small groups to complete given patterns and find the rule for the pattern. The teacher will be observing and helping groups as needed. Day 1 - Once the students have explored the pattern/rule concept, they will work in pairs complete the day 1 worksheet. Day 2 - After the small group exploration the students will work independently to complete the day 2 worksheet. Differentiation: Student Practice Below Level: The students can explore patterns more using shape manipulatives. You could also have the students work with pictures (Pictures of fruit piled up in lieu of the number tiles) to create patterns. Extending this lesson to three days is also recommended for this level of student. Algebra and Patterns 9 Above Level: Have students explore higher number patterns. Have the students create their own pattern using a given rule. (Incorporate the use of calculators for numbers greater then 7 digits) The teacher should close this lesson with some type of real life connection. The class could discuss numerical patterns at the: Closure • gas pump (Unleaded, premium, ultra premium) • soda fountain (Small, medium, large) This is a wonderful introductory lesson for a fourth grade student in to rule, pattern relationships. It allows the student to be hands-on, with the use of the number tiles, but also use higher level thinking, when it Reflection comes to identifying the rules. The lesson addresses all learners and ability levels. Algebra and Patterns 10 Writing an Expression Content Standard and/or English Language Development Standard: Math Strand 3 Concept 3 P.O. 1, Strand 5 Concept 2 P.O. 5 Level/Grade: 4 Content Objective: TSW construct expressions using written and numerical forms and orally read the expression with an accuracy of 80%. Assessment: Completed expressions worksheet, performance of reading expressions to class. Pacing: 1 class period Target Vocabulary/Primary Language Support: expression, variable Materials: Individual whiteboards, dry erase markers, worksheet, pencil, math journal, smartboard or whiteboard, Bloom’s Taxonomy: Remembering Understanding Applying Analyzing Evaluating Creating Multiple Intelligences: Verbal-Linguistic Math-logical Spatial Musical Bodily-Kinesthetic Interpersonal Intrapersonal Naturalist Steps Content The teacher should start the lesson with a math warm-up. The students will all be given either a pattern or a rule. The students will then have a Introduction set time (30-60 seconds) to identify their partner in the classroom based on the pattern/rule combination. This partnership will be used to Algebra and Patterns 11 work on the student practice section later in the class period. This lesson has student's work to write expressions based on numerical and non-numerical cues. One of the main goals of this lesson is to increase a student's mathematical vocabulary. The goal of this lesson is NOT to identify an answer but how to read and dismantle an algebraic expression. The teacher will introduce the terms: Input • algebraic expression: a mathematical phrase containing numbers, variables and operations. • variable: a missing number in an algebraic expression Time should be given for the students to record the definitions of these words in their math journals. The teacher will create 4 sets of cards. The sets will include • Set 1 is the variable group: n, a, b • Set 2 is the operations group: +, -, ×, ÷ • Set 3 is the numbers group: 2, 3, 4, 5 Initially the teacher will have 3 students select 1 card from sets 1-3. The teacher will present the class with the 3 cards in any order Guided Practice (variable, operation, number or number operation or variable). The students will write the long form expression on their white board. The teacher will then have the students present and chorale read the expression aloud. (For variation: using a math word wall, the students could re-read the expression using different vocabulary, more than in lieu of plus, multiplied by in lieu of times) Algebra and Patterns 12 Once the class has read the asked the student's to identify what the expression is asking for them to do. Repeat these steps a few times and then have the students erase their boards. Next on an overhead or whiteboard bring up an expression written in long hand (fifteen times a number equals sixty). Have the students write the expressions using numbers and symbols and present their expression to the teacher. Again a chorale read is done. Repeat for at least 5 examples. In the pairs established earlier, have the students work on completing the worksheet. Differentiation: • Below level: in addition to writing out the expressions in long Student Practice form have the students develop a pictorial way for them to express the expression. • Above level: have the students take a problem and write it again but this time doubling the expression. "Writing in Mathematics" The students will write in their math journals the answer to the following two statements. Closure • I discovered today that... • While working on today's assignment I felt... The purpose of this lesson is to connect the student's mathematical and Reflection verbal-linguistic brains. While some students may be confused that Algebra and Patterns 13 they are not solving problems during this lesson the goal of this lesson is to increase the students high-level thinking skills when looking at expression and not just seeing the numbers as numbers. This lesson sets the foundation for future more complex algebraic problem solving activities. Algebra and Patterns 14 Solving Equations Content Standard and/or English Language Development Standard: Math Strand 3 Concept 3 P.O. 2 Level/Grade: 4 Content Objective: TSW compute various algebraic expressions using the four basic operations on a set of equations with an accuracy of 85%. Assessment: Completed worksheet Pacing: 1-2 class periods Target Vocabulary/Primary Language Support: Evaluate, equation Materials: Projector, Smartboard, Work Packet, Bloom’s Taxonomy: Remembering Understanding Applying Analyzing Evaluating Creating Multiple Intelligences: Verbal-Linguistic Math-logical Spatial Musical Bodily-Kinesthetic Interpersonal Intrapersonal Naturalist Steps Content To introduce the concept, the students will watch the video "Mr. X finds out his value" http://www.youtube.com/watch?v=J2TYyUftI8k. This video gives a brief overview of x trying to find his value by trying to Introduction balance the equation scale. After viewing some discussion questions could be: • What happened when something was done to one side of the Algebra and Patterns 15 equation? • What happens to a number that is touching a parenthesis? • Why did they drop the one in front of the x? The concept of this lesson is to teach the students the concept of equation balancing with an unknown. Introduce the scale/equation Input balance concept. Explain why it is important to have both sides of the equation equal. Using a balance scale on the smartboard/overhead, the teacher will work through solving an equation for the variable. The teacher will then ask the students to work through the equation to keep both sides of the equation equal but also trying to find the value of the equation. Step One: Display the blank scale Guided Practice Step Two: Input an equation the scale with the sides balanced. (The teacher can relate the center fulcrum as an equal sign.) Step Three: Do something to one side of the equation that puts the scale out of balance Algebra and Patterns 16 Step Four: Remind the students that what you do to one side of the equation you must do to the other side of the equation to balance the equation out. Step 5: Complete the math to both sides Repeat the steps for additional problems until understanding is forming. For the student practice students will work in pairs to explore the concept of equation balancing. Using the worksheet and scale manipulatives to guide their exploration. If a second day is needed have students draw the scale themselves to give them another tool Student they could use on a standardized test to help them understand the Practice equation. Differentiation: Below Level: Have students use manipulatives during their exploration. (Borenson's Hands on Equations is a good manipulative to use, Algebra and Patterns 17 http://www.borenson.com/) Technologically Savvy: Using web based resources like NLVM's Virtual Algebra Balance Scales (http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html) students can input the assigned equations to the website and balance the equations using a virtual scale. Above Level: Have students work with equations with variables on both sides of the equation. (The variable should be the same on both sides.) Math Journal: Have the student write about how equations are used in real world situations. Have students think about the unknowns they may experience in their daily life. Examples: • The student knows what shirt and shoes they want to wear but they do not know if they want to wear shorts or pants. How could Closure the variable change the outcome? • The student has $10 to spending at the concession stand at the movies. They already bought a $4 soda. If popcorn costs $5 for a medium and $7 for a large what size could they buy? Could they buy candy, for $2, if they bought popcorn? The goal of this lesson is help the student understand the concept of solving an equation for an unknown. The activities give the student a Reflection visual representation they can use to help explain the process at a later point. Algebra and Patterns 18 Writing Equations for Word Problems Content Standard and/or English Language Development Standard: Math Strand 3 Concept 3 P.O. 2, Math Strand 5 Concept 2 P.O. 5 Level/Grade: 4 Content Objective: TSW covert a word problem to an equation and solve the equation, on a given set of word problems with an accuracy of 85%. Assessment: Completed worksheets Pacing: 1 - 2 Class Periods Target Vocabulary/Primary Language Support: equation Materials: smartboard/projector, worksheet Bloom’s Taxonomy: Remembering Understanding Applying Analyzing Evaluating Creating Multiple Intelligences: Verbal-Linguistic Math-logical Spatial Musical Bodily-Kinesthetic Interpersonal Intrapersonal Naturalist Steps Content To begin the lesson have students think of times in life where they know the answer to problem, and part of the way they got to the answer but they do not know everything. Examples: Introduction Shopping: They know the final price and they know the original price but they do not know how much the discount was or how much they paid in sales tax. Algebra and Patterns 19 Have students read a set of word problems and get rid of all the extraneous information. The students should cross out any extra information, underline important words and circle what the word problem is asking them to do. Example: Input Jasmine bought a gift for her brother. She paid for it with a $10.00 bill. The casher gave her $3.00 back. How much did the gift cost? Repeat this for a few different word problems. Keep the word problem handy for the guide practice portion of the lesson. After running through some of the word problems and indentifying important information, have students start writing equations based on the word problem. Using the example from the input section: Guided Practice Step 1: $10.00 - x = $3.00 Step 2: x + ($10.00 - x) = $3.00 + x Step 3: $10.00 - $3.00 = x Step 4 $7.00 = x Students will work independently to work through a set of word problems. While this is done independently the teacher should be walking around the room observing the students progress and offering Student Practice ideas to help them understand the concepts taught. Differentiation: Below level: Student can work in pairs to solve the word problems. Algebra and Patterns 20 Have the students draw pictures to help them solve the problem. Above level and Early Finishers: Have students write their own word problems, taking from a real world situation and solving for the unknown. Have students share their answers in pairs. Give students questions to ask their teammate like: • Why did you put the variable first? • What made you write the equation that way? Closure • Would the equation be different if you put the variable on the other side of the equal sign. Once students have peer graded their papers have them turn them in for grading. This lesson is a good way to teach writing equations from word problems and also re-teach how to work with word problems, getting all the important information and solving for what the problem asks you to Reflection solve for. In a way the teacher can teach that a major of word problems are algebraic and can be solved by writing equations. Algebra and Patterns 21 Change in Quantity Content Standard and/or English Language Development Standard: Math Strand 3 Concept 4 P.O. 1, Math Strand 4 Concept 4 P.O. 2 & P.O. 4 Level/Grade: 4 Content Objective: TSW describe how the change in one variable effects a second variable by demonstrating the affects of drops of water on a piece of construction paper, with a minimum score for 3 on all required sections of the rubric. Assessment: Completed worksheet, exploration chart and student presentation (rubric) Pacing: 2 - 3 class periods Target Vocabulary/Primary Language Support: millimeters, change in quantity, diameter Materials: construction paper, pipette, water, ruler with millimeter measurement, Bloom’s Taxonomy: Remembering Understanding Applying Analyzing Evaluating Creating Multiple Intelligences: Verbal-Linguistic Math-logical Spatial Musical Bodily-Kinesthetic Interpersonal Intrapersonal Naturalist Steps Content This lesson is an exploration of how changing how much water is dropped on a paper, how the diameter of the water circle created Introduction change. The teacher could introduce the lesson by spilling their coffee on a desk. The teacher will then take a paper towel and place it down Algebra and Patterns 22 on the spill to start cleaning up the spill. Pull the paper towel up and show it to the class and ask the class, how does the water not soak up the entire paper towel when you put it over the spill? Then ask the class, what would happen if I try to clean up more of my coffee? To begin the lesson, introduce the concept of change in quantity, if x changes, y changes. Explore this concept with equations like y=x+2. Using a chart, have one column be x and each row is labeled 1-5. In a second column, give it a header of y, and work out the answer to the equation. Example: X Y Input 1 3 (y=1+2) 2 4 (y=2+2) 3 5 (y=3+2) 4 6 (y=4+2) 5 7 (y=5+2) Have students work in pairs on their own change in quantity equation and table. Students will work in pairs on this assignment. The teacher will have the student's pair up and will do the first few steps together. Once the Guided Practice class is paired up the teacher will pass out all materials to the teams. Algebra and Patterns 23 Step 1: Students fold their construction paper into 6 squares (2 rows, 3 columns). Label each square 1-6. Step 2: Students take pipette and drop 1 drop of water in the first square. Measure the diameter of the circle created from the water droplet, and record information on worksheet. Step 3: Students will repeat for each square, increasing the number of water drops based on the square number (square 2 = 2 drops) and record results Step 4: Students will complete the worksheet after completing the experiment. Step 5: The student pair will compile a short 2-3 minute presentation on their findings. The presentation should include all their findings, the actual construction paper (hence the use of colored water) and any conclusions the students came up with. Student Practice Differentiation: Below level & ELD: For these students I would increase the number of class periods to 3-4. I would have them create a graphic presentation board exploring their findings (similar to a science fair presentation) Above level: In lieu of doing a simple 1 drop extra per square, these students can write their own y = x + n equation and perform the experiment using that equation. For example 2 drops per square number (square 1 = 2 drops, square 2 = 4 drops, etc.) Algebra and Patterns 24 The closure for this lesson will be the lessons and connecting the student's presentations to the concept of change in quantity, the more Closure drops of water, the bigger the circle. After the presentation the teacher can take a survey of the classes findings This lesson has connections to measurement, the scientific process and to the unit's main concept, algebra. Having the students present their findings to the class will not only help them build confidence but Reflection also help the students connect their knowledge to others in the classroom. Algebra and Patterns 25 Worksheets and Materials for Lessons Algebra and Patterns 26 Find the Missing Term Day 1 - Worksheet Find the missing terms and the rule 1) 5, _____, 31, _____, 57, 70, _____ What is the rule? __________________________ 2) 1, 9, _____, 25 , _____, 41, _____ What is the rule? __________________________ 3) _____, 10, 17, _____ , 31 , _____, 45 What is the rule? __________________________ 4) 2, 9, _____, 23, _____, _____, 44 What is the rule? __________________________ 5) 10, _____, 44, _____, 78, 95, _____ What is the rule? __________________________ 6) 78, 68, _____, _____, 38, _____, _____ What is the rule? __________________________ 7) _____, 80, 75, _____, 65, _____, 55 What is the rule? __________________________ 8) 88, _____, 70, _____, 52, 43, _____ What is the rule? __________________________ 9) _____, ______, 77, 57, _____, 27, 7 What is the rule? __________________________ 10) 107, 100, _____, _____, 79, _____, 65 What is the rule? __________________________ Algebra and Patterns 27 Find the Missing Term Day 2 - Worksheet Find the missing terms and the rule 1. _____, 43, 45, 47, _____, 51, 53, 55, _____, _____ What is the rule? __________________________ 2. 16, 20, 24, _____, 32, _____, 40, _____, _____, 52, _____ What is the rule? __________________________ 3. 9; 26; _____; _____; 2,304; 9,216; _____; _____ What is the rule? __________________________ 4. 55, 53, 51, _____, 47, 45, 43, _____, _____, _____, 35 What is the rule? __________________________ 5. 20, _____, 2420, 26620, _____, 3221020, __________ What is the rule? __________________________ 6. 17 , _____, _____, 12393 , _____, 1003833, 9034497 What is the rule? __________________________ 7. 13, _____, 13, 13, _____, 13, _____ What is the rule? __________________________ 8. 13, 104, _____, 6656, _____, 425984, __________ What is the rule? __________________________ 9. _____, 340, 5780, _____, 1670420, 28397140, __________ What is the rule? __________________________ Algebra and Patterns 28 Find the Missing Term - Number Tiles (Example) 2 4 ? ? 10 ? 14 ? Algebra and Patterns 29 Writing an Expression - Worksheet In the right column write the expression using numbers, symbols or words. 1. nine divided by a number 2. x - 17 3. a number times twenty 4. 36 ÷ y 5. the product of five and n 6. sixteen minus a number 7. 18 + x 8. a number times three 9. twice a certain number 10. 18y Mark is 3 years younger then Julie. Write an expression that demonstrates this. Sue has 5 times as many roses as Nell. Which expression shows the number of roses Sue has. 5+n n÷5 5xn Algebra and Patterns 30 Solving Equations - Worksheet Directions: Express the equations using the scale, solve for the unknown, and answer the questions below the scale. Example: 5x + 3=18 (Use shapes to express the unknown.) Step 1: (Express Equation) Step 2: (Remove non-variables from both sides) (In this case subtracting 3) Step 3: (Remove multiples of variable from both side) (In this case dividing by 5) Step 4: (Arrive at answer) Step 5: (Express your answer) x=3 Algebra and Patterns 31 4x + 3 = 15 x = _________________ What is the first step to solve the problem? Would the answer be the same if the problem was 3 + 4x = 15? Algebra and Patterns 32 10x - 13 = 47 x = ______________ How could you solve this problem without the scale? Would the answer be the same if the problem was 13 + 10x = 47? Algebra and Patterns 33 7x + 9 = 58 Draw your own scale and solve for x. x = ____________ Does the problem change when there is a variable on both sides of the equation? Describe a time when you could use an equation in the real world? Algebra and Patterns 34 Writing Equations for Word Problems - Worksheet Directions: Read each problem, cross out any extra information, underline important words and circle what the word problem is asking them to do. Write the equation to represent the word problem and solve for the variable. Your variable can be a shape or a letter. Remember to show your work. 1. Mr. Bill bought 4 boxes of crayons for his students. He bought a total of 48 crayons. If each box has the same number of crayons, how many crayons are in each box. Equation: ___________________________ Answer: ____________________________ 2. Tim's mom bought some packages of hot dog buns for a barbeque at their house. Each package contained 8 buns. She bought a total of 64 buns. How many packages of buns did Tim's mom buy. Equation: ___________________________ Answer: ____________________________ 3. Sydney and Adrianna took a math test. Sydney scored 15 more points then Adrianna. If Sydney scored 94 points, how many points did Adrianna score? Equation: ___________________________ Answer: ____________________________ Algebra and Patterns 35 4. Kennedy bought 12 packages of Pokémon cards. Kennedy spent $36.00 in all. How much was each pack of Pokémon cards? Equation: ___________________________ Answer: ____________________________ 5. Jennifer recently wrote 7 thank you cards to her classmates for coming to her birthday party. She spent a total of 49 minutes writing the cards. How much time did Jennifer spend writing each thank you note? Equation: ___________________________ Answer: ____________________________ Algebra and Patterns 36 Change in Quantity - Worksheet Water Droplets Instructions and Worksheet Step 1: Fold your construction paper into 6 squares (2 rows, 3 columns). Label each square 1-6. Example: Step 2: Take a pipette and drop 1 drop of water in the first square. Measure the diameter of the circle created from the water droplet, and record information on page 2 of the worksheet. Step 3: Repeat step 2 for each square, increasing the number of water drops based on the square number (square 2 = 2 drops) and record results Step 4: Complete the follow-up questions on your worksheet after completing the experiment. Step 5: In your pair, compile a short 2-3 minute presentation on your findings. The presentation should include all their findings, the actual construction paper and any conclusions the students came up with. HAVE FUN! Algebra and Patterns 37 Record you findings here: Square Number of Diameter of circle Observations Number water droplets (in mm) 1 2 3 4 5 6 Notes about your experiment: Algebra and Patterns 38 Follow-up questions: What did you notice about the size of the circles as more water was put into the squares? What is an equation you can use to help you figure out the estimated size of squares 7 and 8? Would anything change if you were to double, or triple, the amount of water you put in each square? What was the variable in this experiment? How would the measurements be different if we used inches or centimeters? What conclusions could you make from this experiment? Algebra and Patterns 39 Presentation Notes: Presentation Checklist: Is your construction paper chart labeled? Are you talking about any conclusions your team came up with? How well did you work with your partner? Do you think you can get a 3 on all items on the rubric? Algebra and Patterns 40 Assessments and Rubrics Algebra and Patterns 41 Solving Equations Quiz Directions: Solve for the unknown. Remember to show your work. Equation Your work Answer 5Y+1 = 26 4Y+20 = 28 5X+0 = 10 4Y+7 = 23 3Z+2 = 20 Y+3 = 7 2Z+12 = 20 Z+21 = 24 Algebra and Patterns 42 Algebra & Patterns Post Test Find the one-step rule then fill-in the missing terms 1. _____, 43, 45, 47, _____, 51, 53, 55, _____, _____ Rule: _______________________________ 2. 16, 20, 24, _____, 32, _____, 40, _____, _____, 52, _____ Rule: _______________________________ 3. 9; 26; _____; _____; 2,304; 9,216; _____; _____ Rule: _______________________________ 4. 55, 53, 51, _____, 47, 45, 43, _____, _____, _____, 35 Rule: _______________________________ Find the two-step rule then fill-in the missing terms 5. 4, 5, 7, 11, 19, _____, _____, 131, _____ Rule: _______________________________ 6. 2, 2, 4, 6, _____, 16, 26, 42, _____, _____, 178 Rule: _______________________________ 7. 3, 8, 18, _____, _____, 158, _____, 638 Rule: _______________________________ 8. 3, 3, 6, _____, 15, 24, _____, 63, _____, 165 Rule: _______________________________ Write the expression in words or in numbers 9. nine divided by a number ___________________ 10. fifteen times a number ___________________ 11. sixty-four more then a number ___________________ 12. 38+w ___________________ Algebra and Patterns 43 Solve the equation 13. 5+ =8 = __________________ 14. - 5 = 11 = __________________ 15. n + 9 = 18 n = __________________ 16. 25 - c = 13 c = __________________ Use the following table to answer the 17-19. x y 5 14 6 17 7 20 8 23 9 26 17. What is the rule for the pattern in column x? __________________ 18. What is the rule for the pattern in column y? __________________ 19. Describe how a change in a number in column x produces a change in a number in column y. ________________________________________________________________ ________________________________________________________________ 20. Kathryn has 6 bookshelves. Each bookshelf has the same number of books B, on it. Which expression shows how many books Kathryn has in all? a. 6 + B b. 6 – B c. 6 x B d. 6 ÷ B Algebra and Patterns 44 Oral Presentation Rubric: Water Droplets (Change in Quantity) CATEGORY 4 3 2 1 Collaboration Almost always Usually listens to, Often listens to, Rarely listens to, with Peers listens to, shares with, and shares with, and shares with, and shares with, supports the supports the supports the and supports efforts of others efforts of others in efforts of others in the efforts of in the group. the group but the group. Often is others in the Does not cause sometimes is not not a good team group. Tries to "waves" in the a good team member. keep people group. member. working well together. Content Shows a full Shows a good Shows a good Does not seem to understanding understanding of understanding of understand the of the topic. the topic. parts of the topic. topic very well. Preparedness Student is Student seems The student is Student does not completely pretty prepared. somewhat seem at all prepared. prepared. prepared to present. Speaks Speaks clearly Speaks clearly Speaks clearly Often mumbles or Clearly and distinctly and distinctly all and distinctly cannot be all (100-95%) (100-95%) the most (94-85%) of understood OR the time, and time, but the time. mispronounces mispronounces mispronounces Mispronounces more than one no words. one word. no more than one word. word. (RubiStar.com 2010) Algebra and Patterns 45 References ALTEC at University of Kansas. (2010). RubiStar Home. Retrieved from http://rubistar.4teachers.org/ Buckle Down Publishing, (2010). Buckle Down Arizona AIMS Mathematics for Grade 4 (4th ed.). Littleton, MA: Buckle Down Publishing. City of Phoenix, Parks and Recreation Department. (2010). Phoenix Public Library. Retrieved from http://www.phoenixpubliclibrary.org/ National Coalition for Parent Involvement in Education (NCPIE). (2010). National Coalition for Parent Involvement in Education (NCPIE). Retrieved from http://www.ncpie.org/ Texas A&M University Corpus Christi. (2010). Middle & High School: Literature in Mathematics. Retrieved from http://sci.tamucc.edu/~eyoung/middle_school_literature.html