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Fourth Grade Algebra and Patterns Lesson Plans

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					                                                        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

				
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Description: A set of 5 lesson plans based on the Arizona state standards for fourth grade alegbra and patterns.