math academy see it

7/29/2019 Math Academy See It

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MaAcamyCan Yu S I in Nau?Explorations in Patterns & Functions


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Congratulations! Youve just ound your answer to the

question, What can I do to create real enthusiasm or

mathematics in all my students?

Created by teachers or teachers, the Math Academy tools

and activities included in this booklet were designed to create

hands-on activities and a un learning environment or the

teaching o mathematics to our students. On Math Academy

days I oten ound that I couldnt make it rom my car to my

classroom without being stopped by enthusiastic students

wanting to know every detail o the upcoming days events.

Math Academy days contributed to a positive school-wide

attitude towards mathematics on our campus.

This booklet contains theMath Academy Can You See It

in Nature? Explorations in Patterns & Functions, which you

can use to enhance your math instruction while staying true

to the academic rigor required by the state standards ramework.

This eort would not have been possible without support rom

The Actuarial Foundation. With the help o the Foundations

Advancing Student Achievement (ASA) grant program, whichis committed to unding projects that enhance the teaching o

mathematics, this Math Academy program came into being.

I sincerely hope that you enjoy implementing the Can You See It in

Nature? Math Academy with your students. When you do, you will

nd that your students engage with mathematics on a whole new

level. The Actuarial Foundation is truly a great partner in urthering

mathematics education!

For the kids!

Kmberly Rmbey, M.Ed., NBCT (Mat)Mathematics Specialist

Phoenix, AZ

I you wish to fnd out more about my experiences with this

and other Math Academies, eel ree to contact me via e-mail

[email protected].

A Letter from te Ator


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When the Math Academy concept was rst developed, it was designed as a hal-day or ull-dayevent which allowed students to deepen their understanding o math while interacting with

volunteers rom the community (see page 24 or ideas on working with community volunteers).The activities we selected or these events were hands-on, standards-based lessons which appliedmathematical principles in real-world scenarios. Each student experienced three to ve activitiesduring the course o the event.

Each Math Academy began with a brie school assembly eaturing a guest speaker who representedthat days particular theme. Themes included math related to restaurants, sports, nature, shopping,ne arts and other topics, as well as ocused on math-related careers. Ater the assembly, studentsrotated to dierent classrooms where they engaged in various activities related to mathematics andthe days coordinating theme.

Included in this booklet is the Math Academy Can You See It in Nature? Explorations in Patterns &Functions, which has all the activities we used or the patterns and unctions Math Academy. This MathAcademy is designed to help students understand the connection between geometric and numerical pat-terns (younger students) as well as between patterns and unctions (older students). You may choose toimplement a grade-level or school-wide Math Academy as we originally designed it, or you may preer toimplement these activities in your own classroom. Whichever ormat you use, keep in mind that the goais to help your students see the relevance o mathematics in real-lie contexts. I you would like moreinormation on the set-up or a school-wide or grade-level Math Academy event, visit The ActuarialFoundations Web site atwww.actuarialfoundation.org/grant/mathacademy.html

Wat s a Mat Academy?


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Math Academy Format

Announce to the students that today they will be working on projects dealingwith patterns and unctions in nature. Discuss the act that patterns can be seenall around us and that looking or patterns and unctions in nature help scientistsmake some o their greatest discoveries. Some people say that mathematics is thescience o patterns, and this may not be ar rom the truth. Patterns o all kinds(numerical, spatial, sequential, etc.) help mathematicians solve problems and makenew discoveries. In school, detecting and creating patterns produces better problemsolvers and ecient students o mathematics. The natural themes selected includesh tails, baby snakes, picnic tables, fower petals and crystals. Although the stu-dents will not be working with real plants and animals, remind them that they willbe ocusing on the math knowledge that is needed learn more about our world.

Math Academy Schedule

Schedule and times may vary depending on format being used.

Opening assembly (optional) 15 minutes

Directions and Math Journals 15 minutes

Activity Rotations 3045 minutes per activity

Assessment and Closure 15 minutes

Opening Assembly/Directions

To build enthusiasm and to ocus attention, have everyone participatein the Math Academy Chant(or younger students):

You and me, we all agree Math is un as you will see!It makes us think, it makes us strong,It helps us learn even when were wrong.

You and me, we all agree Math is un at the Math Academy!

Inucin

Announce to the students that today they will be working on projects dealingwith patterns and unctions in nature. Discuss the act that patterns can be seen allaround us and that looking or patterns and unctions in nature help scientists makesome o their greatest discoveries. Some people say that mathematics is the science

o patterns, and this may not be ar rom the truth. Patterns o all kinds (numerical,spatial, sequential, etc.) help mathematicians solve problems and make new discover-ies. In school, detecting and creating patterns produces better problem solvers andecient students o mathematics. The natural themes include sh tails, baby snakes,picnic tables, fower petals and crystals. Although the students will not be working

with real plants and animals, remind them that they will be ocusing on the pro-cesses in which scientists engage to learn more about our world.

Gus Sak psnain (ina)

Beorehand, arrange or someone who works with plants or animals to talkto the students about the mathematics in nature. Possible guest speakers mayinclude someone rom the game and sh department, a local zoo, or a botanical

Gettng Started

Theme

Patterns and Functions Using Themes Seen in Nature toExamine Algebraic Relationships

Objective

Students will build, extend, describe,predict, graph, and generate rules orpatterns and unctions.


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Use the Procedures section in each activity as a skeleton or the lesson.

Look through the Suggestions or Customizing This Activity section.

Select the suggestion(s) which ts best with the pattern/unctionconcepts on which you want your students to ocus.

TEAChER TipS: CuSTOMiziNG ThESE ACTiviTiES

We asked our students to usegraphic organizers to recordtheir thoughts and ndingsin their math journals. Thiscreates a great connection toour language arts curriculum.

The best results are achievedwhen 45 minutes are allowedin each classroom about 30minutes or the activity and15 minutes or clean-up andrefection. The students can

use their math journals torecord their ndings during theactivities and write refectionson the journals blank pages.

Following the patternactivities in this booklet, youwill nd a student quiz aswell as sample surveys orstudents and teachers so thatyou can evaluate the successo your Math Academy. TheActuarial Foundation would

love to hear all about yoursuccess and will send a $50Scholastic Git Certicate tothe rst 100 teachers whoimplement these activities andsubmit the results. For moreinormation and to downloadthe evaluation orm, go towww.actaralfondaton.org/grant/matacademy.tml.

TEAChER TipSgarden. Although this guest speaker will primarily be ocused on the nature sideo this Math Academy theme, you may want to work with him/her ahead otime to assist with tying in mathematical ideas to the talk.

Use o Math Journals

Students record their ndings in their Math Journals during each activity.These journals should contain all recording sheets or the activities as wellas blank paper or the extension activities. Beore beginning the ActivitiesRotation, students should spend about 10 minutes writing in their math jour-nals, including their refections rom the assembly as well as briefy describing

what they already know about patterns & unctions.

Activities Rotation

I multiple classes are participating in the Math Academy, each classroom shouldhost a dierent activity so students will rotate rom classroom to classroom inorder to complete each activity. I only one class is participating, the students mayrotate rom one activity to the next around the room, or they may do each activityas a whole class, one game ater the other. Activities begin on page 7. For bestresults, plan on three to ve activities or your Math Academy.

Closure and Assessment

Once all activities are completed, the students may return to theirhomeroom classes or nal refections and assessment. See pages 21and 22 or sample quiz and survey.

Key VocabularyPattern

Geometric Pattern

Number Pattern

Growth Pattern

Repeating Pattern

Stage

Recursive Rule

Explicit RuleFunction

Function Table

Horizontal

Vertical

Predict

Coordinate Grid

Coordinate Point

Graph

Discrete

X-axis

Y-axis

Origin

Equilateral Triangle

Square

Rhombus

Trapezoid

Hexagon

Gettng Started (continued)


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The next three pages include activity work pages or your students to use

as they record their thoughts during each activity in this booklet. Page8 displays a ormat or younger students primarily ocused on patterns

while pages 9 and 10 display a two-sided ormat or older students to

use when working on the pattern-unc-

tion connection. The second side o this

sheet provides space or the students to

graph the unction on a coordinate grid.

Use whichever work-page best ts your

instructional objectives (or eel ree to

reormat to t your goals).

Actty Work pages

Activity Work Page:Patterns

Draw and extend the geometric pattern.

Write and label the number pattern(s) to describe an attribute of the geometric pattern above.

Use words to describe the pattern.

Draw and describe the ________ stage of this pattern.

Activity Work Page:Patterns & Functions

Draw and extend the geometric pattern.

Create a function table to describe an attributeo the geometric pattern above.


D raw and des cr ibe the ________ s tage . W hat is the spec if c r ul e or th is unct io n?

continued on other side

10

ActivityWorkPage:Patterns&FunctionsUsethenumbersinthefunctiontablebelowtocreateagraphofthisfunction.CoordinatePoints:

Plotthecoordinatepointsonthegraphbelow. Ifthedataiscontinuous,connectthepointswithaline.

Ifthedataisdiscrete,connectthepointswithadottedline. Besuretoincludeatitleandlabelsforthe

x-andy-axis(bothnumbersandwords).

Title:

0


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Actty Work page:Patterns

Draw and extend the geometrc attern.

Write and label the nmber attern(s) to describe an attribute o the geometric pattern above.


Draw and describe the ________ stage o this pattern.


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Actty Work page:Patterns & Functions

Draw and extend the geometrc attern.

Create a fncton table to describe an attributeo the geometric pattern above.


Draw and describe the ________ stage. What is the specic rule or this unction?

continued on other side


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Actty Work page:Patterns & Functions

Use the numbers in the unction table below to create a graph o this unction.

Coordnate ponts:

Plot the coordinate points on the gra below. I the data is continuous, connect the points with a line.I the data is discrete, connect the points with a dotted line. Be sure to include a title and labels or thex- and y-axis (both numbers and words).

Ttle:

0


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Mat Academy Actty 1:Fish Tails

pATTERN

Objective Students will extend a toothpick pattern and describe thegrowth pattern associated with it. In addition, older students willdescribe the relationships between attributes o the pattern on aunction table, with an equation, and on a coordinate graph.

Materials Toothpicks

Work Page (or blank paper)

Pencils

Procedures 1. Demonstrate the rst our stages o this pattern usingtoothpicks to create the shapes.

2. Ask students to extend the pattern three more stages byadding one more square to the shs tail or each stage.

3. Ask students to record and describe their sh using

picture, words, and numbers.4. Ask students to predict and draw what stage 12 will look

like without building the pattern any urther. They shouldinclude a description o how they gured this out.

Ideas orCustomizingThis Activity

1. Distinguish between a pattern and a unction (a patterndisplays recursion within one set o numbers, usuallydemonstrated with a string o numbers, while a unctiondisplays the explicit relationship between sets o numbers).

2. Translate each geometric relationship into an algebraicexpression or equation.

3. Have students create a unction table demonstrating thenumber o toothpicks used in each stage o the pattern.

4. Ater creating the unction table, ask students to generatethe explicit rule (or unction) which indicates the relation-ship between the two sets o numbers.

5. Use the numbers in the unction table(s) to create coordi-nate points and graph the unction on a coordinate grid.

Teachers Answer KeyExtend the Pattern:

Prediction:Stage 12 will have 36 toothpicks.

Number Patterns:

Toothpicks: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 (recursive rule:add 3 to nd the next number in the pattern start with 3)

Function Table Sample:Function tables may be set up horizontally (as shown here)

or vertically.

Numb ticks a eac Sag

Stage Nmber (n) 1 2 3 4 5 6 7 8 9 10

Tootcks (t) 3 6 9 12 15 18 21 24 27 30

Exlct Rle t= 3n

Fncton (n) = 3n


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Mat Academy Actty :Baby Snakes

pATTERN Objective Younger students will extend a snap cube pattern and describe thenumber pattern(s) associated with it. Older students will recordthe patterns related to a snap cube pattern on unction tables,derive the unctions (explicit ormulas) or those patterns, and/orgraph the unction on a coordinate grid.

Materials Snap cubes in 2 colors(the ends are one color andthe middle are another color)

Paper

Pencils

Procedures 1. Start a growing snake pattern using the snap cubes. Thetwo end cubes should be one color, and all cubes inbetween should be the other color.

2. Snake Patterns:Day 1 red, 2 blues, red

Day 2 red, 4 blues, red



3. Ask students to create the next three stages o this patternusing snap cubes.

4. Ask students to record and describe their blocks usingpictures, words, and numbers.

5. Ask students to predict and draw what stage 12 will looklike. They should include a description o how they guredthis out.


1. Distinguish between a pattern and a unction (a patterndisplays recursion within one set o numbers, usuallydemonstrated with a string o numbers, while a unctiondisplays the explicit relationship between sets o numbers).

2. Translate each geometric relationship into an algebraicexpression or equation.

3. Have students create a unction table demonstrating one

(or more) o the ollowing relationships:

Stage to blue

Stage to total snap cubes

4. Ater creating the unction table, ask students to generatethe unction (or expression) which indicates the relation-ship between the two sets o numbers.

5. Use the numbers in the unction table(s) to create coordi-nate points and graph the unction on a coordinate grid.


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Teachers Answer Key

Extend the Pattern:

Prediction:Stage 12 will have will have 2 reds and 24 blues or atotal o 26 snap cubes.

Number Patterns:Red: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2(recursive rule: add 0 to nd the nextnumber in the pattern start with 2)

Blue: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20(recursive rule: add 2 to nd the nextnumber in the pattern start with 2)

All Blocks: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22(recursive rule: add 2 to nd the next numberin the pattern start with 4)

Function Table Sample:Function tables may be set up horizontally (as shown here) or vertically.

Choose one o the ollowing relationship on which to ocus and usethe others as extensions.

Numb r Cubs in eac Sag

Stage Nmber (n) 1 2 3 4 5 6 7 8 9 10

Red (r) 2 2 2 2 2 2 2 2 2 2

Exlct Rle r= 2

Fncton (n) = 2

Numb Bu Cubs in eac Sag

Stage Nmber (n) 1 2 3 4 5 6 7 8 9 10

Ble (b) 2 4 6 8 10 12 14 16 18 20

Exlct Rle b = 2n

Fncton (n) = 2n

Numb Cubs in eac Sag

Stage Nmber (n) 1 2 3 4 5 6 7 8 9 10

All Blocks (a) 4 6 8 10 12 14 16 18 20 22

Exlct Rle a = 2n + 2

Fncton (n) = 2n + 2

Mat Academy Actty :Baby Snakes


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Mat Academy Actty :Picnic Tables

pATTERN Objective Younger students will extend pattern block patterns and describethe number pattern(s) associated with the perimeter. Older stu-dents will record the patterns related to pattern block perimeterson unction tables, derive the unctions (explicit ormulas) orthose patterns, and/or graph the unction on a coordinate grid.

Materials Pattern blocks (triangles, squares, blue rhombi, trapezoids,hexagons)

Work-pages rom this booklet or blank paper

Pencil

Procedures Preparation: Put pattern blocks into baggies with onlyone shape in each bag a minimum o 6 blocks per bag.

This activity encourages students to examine what hap-pens to the perimeter o each table as the blocks arepushed together to create longer picnic tables.

Ask students to take one shape out o the bag and recordhow many people could sit around that table i one personcan sit at each side.

Next, have students take out one more block and push it upagainst the rst block so that they touch along one ull side(see diagram to the let). Record how many people can sitaround the perimeter o this table with this new conguration.

Have students continue to add one block at a time to theirpicnic tables, always pushing one ull side against the ullside at the end. Record the perimeter or each new table.

1.

2.

3.

4.

5.


You may choose to put the students into groups o 2-4students and have each group use a dierent shape. Thestudents may create posters to display the geometricpatterns, numbers patterns, descriptions, unction tables,and/or graphs or their respective shapes.

Distinguish between a pattern and a unction (a patterndisplays recursion within one set o numbers, usuallydemonstrated with a string o numbers, while a unctiondisplays the explicit relationship between sets o numbers).

Translate each geometric relationship into an algebraicexpression or equation.

Have students create a unction table demonstrating one(or more) o the ollowing relationships:

Triangles to seats(perimeter)

Squares to seats(perimeter)

Rhombi to seats(perimeter)

Trapezoids to seats(perimeter)

Hexagons to seats(perimeter)

1.

2.

3.

4.


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Ideas orCustomizing

This Activity(continued)

Ater creating the unction table, ask students to generatethe unction (or expression) which indicates the relation-ship between the two sets o numbers.

Use the numbers in the unction table(s) to create coordi-nate points and graph the unction on a coordinate grid.

5.

6.

Teachers Answer Key

Prediction:Stage 12 or each pattern will have the ollowing perimeters:

Triangles: 14

Squares: 26

Rhombi: 26

Trapezoids: 26

Hexagons: 50

Number Patterns:Triangles: 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 (explicit rule: add 1 to nd the next numberin the pattern start with 3)

Squares: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 (explicit rule: add 2 to nd the nextnumber in the pattern start with 4)

Rhombi: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 (explicit rule: add 2 to nd the nextnumber in the pattern start with 4)

Trapezoids: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 (explicit rule: add 2 to nd the nextnumber in the pattern start with 4)

Hexagons: 6, 10, 14, 18, 22,, 26, 30, 34, 38, 42, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22(explicit rule: add 4 to nd the next number in the pattern start with 6)

Function Table Samples:

Function tables may be set up horizontally (as shown here) or vertically.Choose one o the ollowing relationships on which to ocus and usethe others as extensions.

Numb Sas a eac Sag - tiangs

Nmber of Trangles (t) 1 2 3 4 5 6 7 8 9 10

Nmber of Seats () (ermeter) 3 4 5 6 7 8 9 10 11 12

Exlct Rle p = t + 2

Fncton (t) = t+ 2

Numb Sas a eac Sag Squas* (same numbers for rhombi and trapezoids just change the variable NOTE: allow students to discover this similarity on their own)

Nmber of Sqares (s) 1 2 3 4 5 6 7 8 9 10


Exlct Rle p = 2s + 2

Fncton (s) = 2s + 2

Numb Sas a eac Sag - hxagns

Nmber of hexagons (h) 1 2 3 4 5 6 7 8 9 10


Exlct Rle p = 4h + 2

Fncton (h) = 4h + 2

Mat Academy Actty :Picnic Tables


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Mat Academy Actty :Flower Petals

Objective Younger students will extend a geometric pattern anddescribe it using numbers and words. Older students willextend a geometric pattern, describe it with numbers usingunction tables, dene the unction as an explicit rule, andgraph the unction on a coordinate grid.

Materials Pattern blocks (hexagons and squares)

Work-page (or blank paper)

Pencils

Procedures Demonstrate the rst three stages o this pattern.

Ask students to extend and record the next three stagesusing pattern blocks.

Ask students to record the number pattern associated withthe number o squares at each stage. You may dene howar they extend the number pattern (10 stages works well).

Ask students to predict, record, and describe what stage10 will look like.

1.

2.

3.

4.


Distinguish between a pattern and a unction (a patterndisplays recursion within one set o numbers, usuallydemonstrated with a string o numbers, while a unc-tion displays the explicit relationship between sets onumbers).

Translate each geometric relationship into algebraicexpression or equation.

Have students create a unction table demonstrating thenumber o squares used in each stage o the pattern.

Ater creating the unction table, ask students to generatethe explicit rule (or unction) which indicates the rela-tionship between the two sets o numbers.


1.

2.

3.

4.

5.

pATTERN

Stage 1:

Stage 2:

Stage 3:


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Teachers Answer Key

Extend the Pattern:

Prediction:Stage 10 will have 54 squares (9 squares lined up on each side o the hexagon)

Number Patterns:Squares: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54 (recursive rule: add 6 to nd the nextnumber in the pattern start with 0)

Function Table Sample:Function tables may be set up horizontally (as shown here)or vertically.

Numb Squas a eac SagStage Nmber (n) 1 2 3 4 5 6 7 8 9 10

Sqares (s) 0 6 12 18 24 30 36 42 48 54

Exlct Rle s = 6(n - 1)

Fncton (n) = 6(n - 1)

Mat Academy Actty :Flower Petals


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Mat Academy Actty : Growing Crystals

Objective Younger students will extend the patterns using square tilesand describe the number pattern(s) associated with it. Olderstudents will record the pattern related to square tile patternon a unction table, derive the unction (explicit ormula) orthat pattern, and graph the unction on a coordinate grid.

Materials 1-inch or 1-cm squares in two colors

Work-page (or blank paper)

Pencil

Colored pencils (optional)

Procedures Demonstrate the rst 3 stages o the growing crystals

pattern using squares.Ask students to continue the next three stages o the pat-tern using squares.

Ask students to draw their results and describe the pat-tern using numbers and words.

Ask the students to draw and describe what the patternwould look like at stage 10.

Repeat with Pattern 2.

1.

2.

3.

4.

5.

Ideas or

CustomizingThis Activity

Distinguish between a pattern and a unction (a patterndisplays recursion within one set o numbers, usuallydemonstrated with a string o numbers, while a unctiondisplays the explicit relationship between sets o numbers).

Translate each geometric relationship into an algebraicexpression or equation.

Have students create a unction table demonstrating one(or more) o the ollowing relationships:

Number o dark squares at each stage

Number o light squares at each stage

Number o total squares at each stage

Ater creating the unction table, ask students to generatethe explicit rule (or unction) which indicates the rela-tionship between the two sets o numbers.


1.

2.

3.

4.

5.

pATTERN 1

Stage 1:

Stage 2:

Stage 3:

pATTERN

Stage 1:

Stage 2:

Stage 3:


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Teachers Answer Key

pan 1:

Extend the Pattern:

Prediction:Stage ten will have 10 dark squares and 26 light squares, or a total o 36 squares

Number Patterns:Dark Squares: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (recursive rule: add 1 to ndthe next number in the pattern beginning with 1)

Light Squares: 8, 10, 12, 14, 16, 18, 20, 22, 24, 26(recursive rule: add 2 to nd the next number in the pattern beginning with 8)

Total Squares: 9, 12, 15, 18, 21, 24, 27, 30, 33, 36(recursive rule: add 3 to nd the next number in the pattern beginning with 9)

Function Table SamplesFunction tables may be set up horizontally (as shown here) or vertically.

Choose one o the ollowing relationships on which to ocus and usethe others as extensions.

Numb dak Squas in eac Sag

Stage Nmber (n) 1 2 3 4 5 6 7 8 9 10

Dark Sqares (d) 1 2 3 4 5 6 7 8 9 10

Exlct Rle d =n

Fncton (n) =n

Numb lig Squas in eac Sag

Stage Nmber (n) 1 2 3 4 5 6 7 8 9 10

Lgt Sqares (l) 8 10 12 14 16 18 20 22 24 26

Exlct Rle l = 2n + 6

Fncton (n) = 2n + 6

Numb Bcks in eac Sag

Stage Nmber (n) 1 2 3 4 5 6 7 8 9 10

Total Sqares (t) 9 12 15 18 21 24 27 30 33 36

Exlct Rle t= 3n + 6

Fncton (n) = 3n + 6



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Teachers Answer Key (continued)

pan 2:

Extend the Pattern:

Prediction:Stage ten will have 100 dark squares and 44 light squares or a total o 144 squares.

Number Patterns:Dark Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 (recursive rule: add consecutiveodd numbers (beginning with 3) to the previous number to nd the next numberin the pattern start with 1)

Light Squares: 8, 12, 16, 20, 24, 28, 32, 36, 40, 44 (recursive rule: add4 to nd the next number in the pattern start with 8)

Total Squares: 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 (recursive rule: addconsecutive odd numbers (beginning with 7) to the previous number to ndthe next number in the pattern start with 9)

Function Table SamplesFunction tables may be set up horizontally (as shown here) or vertically.

Choose one o the ollowing relationships on which to ocus and use theothers as extensions.

Numb dak Squas in eac Sag

Stage Nmber (n) 1 2 3 4 5 6 7 8 9 10

Dark Sqares (d) 1 4 9 16 25 36 49 64 81 100

Exlct Rle d =n2

Fncton (n) =n2

Numb lig Squas in eac Sag

Stage Nmber (n) 1 2 3 4 5 6 7 8 9 10

Lgt Sqares (l) 8 12 16 20 24 28 32 36 40 44

Exlct Rle l = 4n + 4

Fncton (n) = 4n + 4

Numb Bcks in eac Sag

Stage Nmber (n) 1 2 3 4 5 6 7 8 9 10

Total Sqares (t) 9 16 25 36 49 64 81 100 121 144

Exlct Rle T= (n + 2)2

Fncton (n) = (n + 2)2



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1. What job would you like to have when you grow up?

2. What kind o math skills do you think you will need to do that job?

3. Rank each o these statements on a scale o 1 to 5 (1 being lowest rank):

I like math in school. 1 2 3 4 5I use math outside o school. 1 2 3 4 5

The math I learn at school is helpul. 1 2 3 4 5

I am good at math. 1 2 3 4 5

I liked participating in the Can You See It in Nature? 1 2 3 4 5

I learned a lot about math during the Math Academy. 1 2 3 4 5

I would like to participate in Math Academiesagain in the uture. 1 2 3 4 5

4. The best thing about the Math Academy was:

5. The worst thing about the Math Academy was:

6. Do you know what an actuary is?

Samle Stdent Srey


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1. What ormat did you use or this Math Academy?

m classroom m all classrooms in grade level m school-wide to all grade levels

2. What grade-level(s) used this Math Academy lesson?

3. Which Math Academy activities did you utilize with your students? 1 2 3 4 5 6

4. For the ollowing two questions, please use a ranking scale o 1 through 5(5 = great; 3 = mediocre; 1 = poor).

Overall, how would you rank this Math Academy?

How would you rank the activities you presented/taught?

5. Would you recommend these activities be used again?m Yes m No

Comments:

6. Do you think your students now have a better understanding o patterns and unctions?

m Yes m No

Comments:

7. Would you like to participate in another Math Academy?

m Yes m No

Comments:

8. Please let us know how well your Math Academy went.

9. Comments, ideas, suggestions:

Samle Teacer Srey


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One o the most benecial aspects o our Math Academy program is theactuarial mentors/volunteers who interact with our students during eachMath Academy activity. Our actuarial mentors take time away rom theirusual work responsibilities on the days o our events so they can help out inthe classrooms. Please take the time to contact The Actuarial Foundation [email protected] to nd out i actuaries are available in your area.

I you do not have actuaries available in your community, you may want toconsider requesting the assistance o parents, community members, or busi-ness partners who would be willing to work with the students during theactivities.

Ater securing your mentors/volunteers, it is critical to identiy a Lead Mentorwho will serve as the liaison between you and the other mentors. The Lead

should e-mail all communications rom the teachers to the mentors, set upschedules, send reminders beore each event, etc.

Mentor Training Session

Distribute the Math Academy schedule.

Distribute copies o the Math Academy activities.

Pedagogy Discuss some simple teaching techniques.

Management Assure mentors that the teachers willhandle all discipline. Discuss preventative managementtechniques such as proximity and having activities

well-prepared to avoid student down-time.

Brainstorm Allow some time during your trainingto take any ideas or suggestions rom your mentors.

Allow time or questions and answers.

Assigning mentors Assigning mentors to the sameclassroom throughout the year will help build stronger relationships withthe students and teachers.

E-mail exchange Collect everyones e-mail addresses oreasy communication between mentors and teachers.

School tour End your training with a school tour. Be sureyour mentors know the key locations o your school includingthe sign-in book (and procedures), restrooms, principals oce,and classrooms. I possible, include a map in their take-homematerials so they can nd their teachers classrooms oncethey receive their assignments.

Commnty inolement

An actuary is an expertwho deals with numbersand percentages, also knownas statistics. Actuaries provideadvice to businesses,governments, and organizationsto help answer questions aboutwhat to expect in planningor the uture.

To nd out more aboutthe actuarial proessionvisit BeAnActary.org.

WhAT iS AN ACTuARY?

The number o volunteer mentorsyou have will depend upon the

ormat and number o studentsinvolved in the program.Although you dont needvolunteer mentors at the class-room level, students nd thesevolunteer mentors to be un.

TEAChER TipS


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The unit included in this Can You See It in Nature? booklet takes intoaccount all o the process standards outlined in NCTMsPrinciples andStandards or School Mathematics (NCTM, 2000), including communica-tion, connections, problem solving, reasoning and proo, and representa-tion. Reerences to those types o processes are made throughout theactivities. As or the content standards, the primary concentration is onAlgebra (specically,Patterns and Functions). The perormance objectivesor each o these areas include the ollowing:

Instructional programs rom pre-kindergartenthrough grade 12 should enable all students to

Understand patterns, relations, and unctions.

Represent and analyze mathematical situationsand structures using algebraic symbols.

Use mathematical models to represent andunderstand quantitative relationships.

Analyze change in various contexts.

In grades 3-5, students should be able to

Describe, extend, and make generalizations aboutgeometric and numeric patterns.

Represent and analyze patterns and unctions,

using words, tables, and graphs.

In grades 6-8, students should be able to

Represent, analyze, and generalize a variety o patterns withtables, graphs, words, and, when possible, symbolic rules.

Relate and compare dierent orms o representationor a relationship.

Identiy unctions as linear or nonlinear and contrasttheir properties rom tables, graphs, or equations.

You will want to check with your own state ramework

to select perormance objectives which are specifc

to your students.

Algnment wt Standards


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Can You SeeIt in Nature?Math AcademyChecklist

Determine the date, time,and schedule or yourMath Academy

Identiy the objectives to

be reinorced through thisMath Academy

Plan the opening assembly,i applicable

Conrm the schedule andcontent with guest speaker,i applicable

Customize the activitiesenclosed in this booklet

Make copies o the activities,quiz and surveys

Purchase and/or gathermaterials

Pattern Blocks

Toothpicks

Snap cubes

1-inch Squares

Pencils

Colored pencils(optional)

Make math journalsor all students

Distribute materialsto other participatingteachers, i applicable

Notes


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More Resources romTeActaral Fondaton

BESTPRACTICESGUIDE

Students achieve with ASA grants

Students and Mentors:A Powerful Combination

Octavio,Grade8All AboutAlgebra

Erica,Grade11Pumped AboutProbability

Katie,Grade5Having FunWith Fractions

Expect the Unexpected with Math

Shake, Rattle, & Roll and Bars, Lines, & Pies, educationalprograms unded by the Foundation and developed anddistributed by Scholastic, the global childrens publishingeducation and media company, are designed to provideteachers and students with math literacy-based materialsthat meet national standards and are in alignment withcore school curriculum. These skill-building programsprovide lesson plans, activities and other teachingresources while incorporating and applying actuariesnatural mathematics expertise in real world situations.

To learn more about the program, or to downloada copy, visit tt://www.actaralfondaton.org/grant/ndex.tml.

Advancing Student Achievement Grants

Advancing Student Achievement helps support youreorts in the classroom by integrating hands-on,practical mathematics skills brought to lie by practicingproessionals into your everyday curriculum.

As part o that program, The Actuarial Foundation oersunding o mentoring programs that involve actuaries insupporting your schools teaching o mathematics.

For inormation on this program and to nd outhow you can apply or an ASA grant, visitwww.actaralfondaton.org/grant/.

Best Practices Guide

This guide eatures a compilation o research on thevalue o mentoring, combined with 15 case historieso programs unded by the Foundation, each o whichincludes inormation on program design and results.

To request a hard copy o the Best Practices Guide, sendan e-mail to [email protected] or to download a copy, visitwww.actaralfondaton.org/grant/bestractces.tml.

Math


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475 North Martingale RoadSuite 600Schaumburg, IL 60173-2226

PH: 847.706.3535FX: 847.706.3599

www.actuarialoundation.org

math academy see it

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