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Find an item in nature and bring it in. Explain using google docs how your item explains Fibonnaci's sequence or draw a diagram. If you cannot bring in the item (like rabbits for the example above) you may draw a diagram like the one above.

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Fibonacci's Rabbits

In the West, the Fibonacci sequence first appears in the book Liber Abaci (1202) by Leonardo of Pisa, known as Fibonacci. Fibonacci considers the growth of an idealized (biologically unrealistic) rabbit population, assuming that:

1. a single newly born pair of rabbits (one male, one female) are put in a field;

2. rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits;

3. rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month on.

The puzzle that Fibonacci posed was: how many pairs will there be in one year?

Suppose we let the number of rabbit pairs in the field at the end of the $n^{\text{th}}$ month be denoted by $F_n$.

Consider just the new "baby rabbit pairs" in the $n^{\text{th}}$ month. They must be equal in number to the pairs of rabbits that are mature enough to give birth to baby rabbits. This, of course, is precisely the number of rabbit pairs alive two months previously, $F_{n-2}$.

Now the total number of rabbit pairs in the $n^{\text{th}}$ month is the number of pairs alive in the previous month (i.e., $F_{n-1}$) plus the number of new baby rabbit pairs, $F_{n-2}$.

Thus, we have the following recursive definition for the $n^{\text{th}}$ Fibonacci number, $$F_0 = F_1 = 1$$ $$F_n := F_{n-1} + F_{n-2}$$

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In the West, the Fibonacci sequence first appears in the book Liber Abaci (1202) by Leonardo of Pisa, known as Fibonacci.

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Make up a playground game using expressions and equations to teach to the class.

FOR EXAMPLE; Teacher puts students in groups of 4. One student is the recorder, two are the runners and one is the "solver". One student will choose a card from the bag and run across the lawn to the other bag of the same color and the "solver". The "solver" student will find the answer they are looking for in the bag and will give it to the runner to run back to the recorder. The recorder will take and glue down on the chart paper both cards together. The next runner will then run back down and repeat the process again. This continues until all cards are matched up. The first time to win will be the fastest and have the most correct pairs.

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Algebra Expression and Equation Card Game Activity or Station by Miss Middle School Teacher

These cards are a great way for middle school students to practice matching verbal models with algebraic/variable expressions and equations.

Students can use these in several ways:

1) When students finish an activity early, they can grab a set of flashcards and practice matching the verbal phrases with the algebraic expression or equation.

2)Students can partner up to match the verbal model to the algebraic expression/equation. Then, they can play 'Go Fish''. They deal 4 cards to each person and place the rest in a messy pile face down for all to reach. They then ask questions, like: "Do you have the the algebraic expression for one half of a number plus three?". Their partner may reply, "Yes, I have 1/2x + 3." Or, "No, go fish!". When a pair is found, the partner takes the pair. Once all pairs have been matched, students count their pairs. The person with the greatest number of pairs at the end wins!

3) Students can partner up to match the terms to the definitions. Then, they play 'Memory''. They place all cards face down on the table in rows. The first partner turns over two cards (leaving them in their position). If the term and definition match, they keep the pair. If not, they turn them back over and hope to remember their location for later. Play continues until all matches have been found. The person with the greatest number of pairs at the end wins!

4) Students can also play "Memory" individually with themselves and try to 'beat the clock'. They can set a time limit for themselves (i.e. 2 minutes) and see if they can find all of the matches in that time.

Included: 32 cards (1 black and white copy, 1 color copy) and a copy of the teacher activity ideas listed above.

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Algebraic Expressions and Equations Card Game Activity or Station

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Algebra Expression and Equation Card Game Activity or Station by Miss Middle School Teacher These cards are a great way for middle school students to practice matching verbal models with algebraic/variable expressions and equations. Students can use these in several ways: 1) When students finish...

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Watch the video above on how to solve a challenging Singapore math problem. Work with your group to solve the problem below on chart paper with markers. Be sure to include pictures/diagrams, equations and a 3/4 sentence paragraph explaining your work and answer.

Problem: There were x children and half as many adults as children at a library in the morning. An hour later, three times the number of children and 40 adults visited the library.
(a) How many people were at the library altogether?
(b) If x=56, find the total number of people at the library.

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0:00 / 8:25•Watch full video

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Singapore Math - Algebra - using models to solve word problems - Primary 5, Primary 6

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Teach a 6th grader how to use a calculator to solve a multistep equation. Your set of directions must include how to solve the equation you came up with and be at least 5 steps in length (written on chart paper). Your equation must also include one variable on both sides and at least 5 terms. Watch the youtube video above for some ideas.

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Makeup 10 puns using math vocabulary terms found in our expressions and equations unit. Write your puns down on a piece of poster board with markers to hang up in the classroom. See the link above for some ideas. DO NOT COPY!

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When kids want to laugh, they rarely turn to their math homework for jokes. But if you're a math teacher or a parent trying to help your kids (keyword: trying) with their math homework, you know a good laugh is exactly what the doctor ordered. These funny math jokes for kids are proof (get it?) that math can be a great source of humor - and humor, it turns out, might even help with those math skills. Recent studies have shown that laughter helps us to learn new things by reducing anxiety and boosting motivation, participation, perception, memory, and attention. Even when math isn't fun, math jokes can be. And because the success of funny math puns depends on understanding the concept behind the punchlines, even corny math jokes are also clever ways to check that your kid understands what they're learning from their math teachers, whether it's geometry, algebra, or prime numbers. And if they're really advanced, you can integrate some calculus jokes into your repertoire.

These math jokes and puns are split into beginner and advanced levels, so you can find the right corny joke for your audience. And if our calculations are correct, these funny math jokes are some of the smartest and easiest-to-remember examples of math humor out there. Whether you're looking for statistics puns or calculus jokes, odds are we've got you covered.

Beginner and Intermediate Math Jokes

1. Why was the math book sad? It had a lot of problems.

2. What did the spelling book say to the math book? "I know I can count on you!"

3. Why did the two fours skip lunch? They already eight!

4. Are monsters good at math? Not unless you Count Dracula.

5. What is the butterfly's favorite subject in school? Mothematics.

6. How do you make time fly? Throw a clock out the window!

7. Why is six afraid of seven? Because seven eight nine!

8. How do you make seven even? Subtract the "S."

9. Why did seven eat nine? Because you're supposed to eat three squared meals a day!

10. What do you get when you multiply a New York City landmark by itself? Times Square.

11. What do you call an adventurous number? A roamin' numeral.

12. How are a dollar and the moon similar? They both have four quarters!

13. Did you hear the one about the statistician? Probably.

14. Why was the student upset when his teacher called him average? It was a mean thing to say!

15. Why was the fraction worried about marrying the decimal? Because she would have to convert.

16. Why is the obtuse triangle always so frustrated? Because it's never right.

17. Why was the equal sign so humble? Because she knew she wasn't greater than or less than anyone else.

18. What do you call a number that can't stay in one place? A roamin' numeral.

19. What did one math book say to the other? "Don't bother me. I've got my own problems."

20. What is a math teacher's favorite snake? A pi-thon.

21. What do you call the number seven and the number three when they go out on a date? The odd couple (but seven is in his prime).

22. Why was the math teacher suspicious of prime numbers? They were all odd.

23. Why can't you trust a math teacher holding graphing paper? They must be plotting something.

24. What is a math teacher's favorite sum? Summer.

25. Which weighs more, 16 ounces of soda or a pound of solid gold? They both weigh the same.

26. Why did the student trust his abacus? She could always count on it.

27. Why do plants hate math? It gives them square roots.

28. What do you call dudes who love math? Algebros.

29. Why should you never talk to Pi? Because she'll go on and on and on forever.

30. Why are parallel lines so tragic? They have so much in common, but they'll never meet.

31. Dear Algebra, stop trying to find your x. They're never coming back - don't ask y.

32. There are three kinds of people in the world: Those who can count and those who can't.

33. How do you stay warm in any room? Just huddle in the corner, where it's always 90 degrees.

34. Why does nobody talk to circles? Because there is no point.

35. What do you call a tea kettle whistling on the top of a mountain? A high-pot-in-use.

36. Did you hear about the mathematician who is afraid of negative numbers? She'd stop at nothing to avoid them.

37. Teacher: "Why are you doing your multiplication on the floor?" Student: "You told me not to use tables."

38. After a sheepdog chased all the sheep into the pen, he told the farmer, "All 40 accounted for." "But I only have 36 sheep," the farmer replied. "I know," said the sheepdog. "But I rounded them up."

39. Why did the triangle make the basketball team? It always made three-pointers.

40. Why did the kid always wear glasses during math class? They improve di-vision.

41. What do you get when you divide the circumference of a jack-o'-lantern by its diameter? Pumpkin Pi!

42. A clerk at the butcher shop is 6 feet tall and wears size 10 shoes. What does he weigh? Meat. He works at the butcher's shop.

1. Why can't you trust a math teacher? They're always calculating.

2. Where did the geometry teacher go on vacation? Who knows? All I know is that she's polygon.

3. What did the math teacher say when his parrot escaped? "Polygon."

4. Why didn't the quarter jump off a bridge with the dime? It had more cents.

5. What geometric shape removes spells and curses? A hexagon.

6. Have you ever noticed what's odd? Every other whole number.

7. What's the best tool for math? Multipliers.

8. What's a swimmer's favorite math? Dive-ision.

9. What do a year and a dollar have in common? They both have four quarters.

10. What's in charge of geometry? The ruler.

11. What's the best way to get a math tutor? An add.

12. What's the most adventurous type of number? Roamin' numerals.

1. Pi was fighting with an imaginary number: "Get real," pi said. "Be rational," the imaginary number said.

2. What do you call an angle that's gone through the garbage disposal? A wrecked-angle.

3. A student turned in a blank sheet of paper for his math test, and the teacher asked him why. "It was on imaginary numbers," he said. "Can't you see them?"

4. There's a fine line between a numerator and a denominator... But only a fraction would understand.

5. What's a math teacher's favorite kind of tree? Geometry.

6. How do you get from point A to point B? Just take an x-y plane or a rhom'bus.

7. Why should you never mention the number 2,885? Because it's "two" gross.

8. Why couldn't the angle get a loan? Its parents wouldn't cosine.

9. Did you hear about the statistician who drowned crossing the river? It was 3 feet deep - on average.

10. I'll do algebra, and I'll do trig. I'll even do statistics. But graphing is where I draw the line!

11. What's the best way to flirt with a mathematician? Use acute angle.

12. What do baby parabolas drink? Quadratic formula.

13. Why did the chicken cross the Mobius Strip? To get to the same side.

14. What's the best way to serve pi? A la mode. Anything else is mean.

15. What do you get when you divide the circumference of the sun by its diameter? Pi in the sky.

16. The problem with math puns is that calculus jokes are all derivative, trigonometry jokes are too graphic, algebra jokes are usually formulaic, and arithmetic jokes are pretty basic. But I guess the occasional statistics joke is an outlier.

17. An engineer, a physicist, and a mathematician are staying in a hotel. The engineer wakes up and smells smoke. He goes out into the hallway and sees a fire, so he fills a trash can from his room with water and douses the fire. He goes back to bed. Later, the physicist wakes up and smells smoke. He opens his door and sees a fire in the hallway. He walks down the hall to a fire hose and, after calculating the flame velocity, distance, water pressure, trajectory, etc., extinguishes the fire with the minimum amount of water and energy needed. Later, the mathematician wakes up and smells smoke. He goes to the hall, sees the fire, and then the fire hose. He thinks for a moment and then exclaims, "Ah, a solution exists!" and then goes back to bed.

18. There are three people applying for the same job at a bank: a mathematician, a statistician, and an accountant. The interviewing committee asks the mathematician one question: "What is 500 plus 500?" The mathematician answers "1,000" without hesitation, and they send him along. Next, they call in the statistician and ask the same question. He thinks for a moment and answers, "1,000... I'm 95% confident." When the accountant comes in, he is asked the same question: "What is 500 + 500?" He bows and replies, "What would you like it to be?" They hire the accountant.

19. What do you call a mathematician who spent all summer at the beach? A tan gent.

20. What do you call a political party in favor of agriculture? Pro-tractors.

21. What do you call more than one L? A parallel!

22. Why wasn't the geometry teacher at school? Because she sprained her angle.

23. What shape is usually waiting for you inside a Starbucks? A line.

24. How does a mathematician plow a field? With a protractor.

25. Why was math class so long? The teacher kept going off on a tangent.

26. What did the zero say to the eight? "Nice belt!"

27. Why do teenagers travel in groups of three and fives? Because they can't even.

28. Why was algebra so easy for the Romans? X was always 10!

29. What English king invented fractions? Henry the 1/8.

30. Why didn't the hyperbola feel sick? It was asymptote-matic.

31. I would tell you a joke about an infinite line... But it doesn't have an endpoint.

32. Have you heard the latest stats joke? Probably...

33. What do parallel lines and vegetarians have in common? They never meat.

34. Why shouldn't you let advanced math intimidate you? It's easy as pi!

35. Why did the mathematician spill all of his food in the oven? The directions said, "Put it in the oven at 180 degrees."

36. Why can't you trust a polynomial to stay the same? They have too many variables.

37. What was the geometry teacher's favorite dance? The rhombus.

38. What do you call a 12-inch nose? A foot.

39. Why do numerators and denominators disagree? They've drawn a line.

40. What geometric shape is lying in wait? A trapezoid.

41. What do you get when you add 2n to 2n in French? It sounds 4n to me, too.

42. Did you hear about the statistician who drowned in the lake? On average, most of it was over his head.

43. What did the triangle say to the circle? "You're pointless."

44. What do you call a student who's great at algebra? An X-pert.

45. Three statisticians are hunting, and they come upon a deer. The first aims and overshoots. The second undershoots. The third then shouts, "We got him!"

46. Did you hear about the statistician who drowned? The pool was 3 feet deep, on average.

47. What is the integral of one divided by a cabin? Log cabin? No, houseboat - you forgot the C.

48. An infinite number of mathematicians walk into a bar. The first tells the bartender he'll have a beer. The second asks for half a beer, and the third requests a quarter. After the barman places two beers in front of all of them, they say, "That's all you're giving us?"

Advanced Math Jokes

The bartender says, "Come on, guys. Know your limits."

1. What do geometry teachers have decorating their floor? Area rugs!

2. What tool is best suited for math? Multi-pliers.

3. A father noticed his son was sad coming home from school one day. "What's wrong?" The father asked. "I really don't like long division," the son answered. "I always feel bad for the remainders."

Not subscribed to Fatherly's newsletter yet? We're not mad, just disappointed.

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Have You Heard the One About the Statistician?

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When kids want to laugh, they rarely turn to their math homework for jokes. But if you're a math teacher or a parent trying to help your kids (keyword: trying) with their math homework, you know a good laugh is exactly what the doctor ordered. These funny math jokes for kids are proof (get it?)

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Use guided imagery to see complex story problems involving expressions and equations. See the website above on what guided imagery looks like. Use chart paper and markers to complete the problem below.

Your problem is :

1. The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle?

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Wallisch began creating moving mathematical images for himself using technical computing environment Matlab, and said that, although he uses it for high-level research computations, high school students can just as easily build visual mathematical models with some guidance. By creating images of equations and playing with the variables, Wallisch now sees what all the fuss is about. He wrote in a blog post: "Personally, I'm betting on aesthetics, with Kant: 'Beautiful is that which is appealing without interest.' As we can't presume interest, aesthetics can serve as an important bridge(head)."

California College of the Arts math professor Michael S. Schneider agreed that imagery is the best way to show students the beauty of math. He has been helping students connect mathematics to visual imagery for nearly forty years, and wrote the book A Beginner's Guide to Constructing the Universe: Mathematical Archetypes of Nature, Art and Science to show humans are surrounded with mathematical imagery -- including right outside, in nature.
[RELATED: How to Deal With Kids' Math Anxiety]
"As a youngster I wasn't particularly outstanding in math," he said. "But at 16 I became earnestly interested in the variety of shapes nature produced and wanted to understand why regular shapes keep recurring in nature. I remember pondering the same hexagonal shape found in the beehive, quartz crystal and metal hexnuts. I could understand how a crystal grew mechanically in this precise geometry by accumulating atoms, but how did bees know how to produce the pattern which holds more weight of honey than, say, a checkerboard pattern? I wasn't comfortable with the 'trial and error' explanation, and even if it was in their DNA, how did that knowledge of superior design get there?" Then, he said, he wanted to know more about logarithmic spirals - "in the bathtub, swirling leaves, tornadoes, hurricanes, solar systems, galaxies." Schneider said he had good math teachers, but these topics were never covered in school; books he looked up on the subjects covered them one at a time, but never altogether in the same place.

Schneider said he became obsessed with understanding the language and shapes of "nature's geometric alphabet": circles, spheres, triangles, squares, and more -- the shapes that surround us every day if we simply take the time to notice them. "A circle represents the number one," he said. "Most people can feel why a circle represents unity, its wholeness, completeness. A circle holds more inside it than any other shape having the same perimeter. So it's practical to know that round pizzas hold more toppings than squares or rectangles having the same length of crust."

Armed with this set of nature's images and symbols, Schneider found that numbers and shapes have personalities, each playing different roles in the cosmos. "The universe becomes a book and then a great play with great actors in great parts telling great stories," he said. "Mathematics is a way to read the world of nature and technology around us. If a teacher can convey this, the entire world becomes an exciting textbook."

Schneider admits that today's math teachers are strapped for time and resources to really explore the beautiful part of math, partly due to the way textbooks are constructed, and the pressure to cover material quickly. He believes that for students to see the beauty in math, teachers need more time and freedom. "I think that math education gets too abstract too quickly without first providing a sense-based foundation," he said.

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Imagery: A Key to Understanding Math | KQED

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According to math educators, mathematical imagery is what students are missing, and what causes confusion. "Mathematics is a way to read the world of nature and technology around us. If a teacher can convey this, the entire world becomes an exciting textbook."

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Create a short 3 question quiz solving math equations/expressions on google forms. Survey 50 people or more and graph the results on google sheets. You must turn in your quiz results and graphs for a grade.

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Create your own youtube video rapping about solving expressions or equations. Video must be 2 minutes in length and you must have your lyrics typed out and turned in.

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Math Rap Dougie - Teach Me How to Solve It (Equations)