INQUIRY

I'm continuing a writing group from last year during Focus.

We've gotten through the beginning of Chapter 8. Here's what we'll be sharing on the last class day:

**At long last, she would have Dr. Moonflower in her power. For years she’d known that he was lurking in some lair, the infection spreading until he was possessed nearly entirely, just as Manchineel was. Moonflower wanted to rise to the top of the food chain—he always had—ever since that day so long ago…**

**She’d been riding her tricycle in the garden with Tarax bounding alongside. Manny the gardener had been raking under the huge Manchineel tree, careful not to touch it or the tiny apples that lay scattered on the lawn. Over by the laboratory windows, she saw her mother’s assistant, Dr. Moon struggling to prune the vines with white flowers that her parents had warned her not to go near. **

**He seemed to be getting wrapped up in the vines as he worked, and he was muttering under his breath, trying to yank the vines further from the house without tripping. Carnivora was sure that the vines were moving, wrapping themselves around his limbs as fast as he could push them away. He began to struggle. He began to run. He began to scream.**

**As he ran, the vines followed and continued to grab his fleeing form, strangling his arms and legs and even his neck. He fell. Desperate, clawing at his neck, he pulled his lighter from his pocket and set the flame against the vines. The vines seemed to shriek with anger and all at once they hurled the man towards the tree. His shirt caught on fire, and as he crashed into the brittle branches of the Manchineel tree, the tree went up in flames. **

**The vines plucked the terrified man from the ground, smothering the flames of his shirt. But they were not trying to help him. The vines, alive with eerie white flowers, were mercilessly pulling him back toward the building as he shrieked and wailed in terror. The tree flamed, smoke rose, and Manny began to choke and gasp, his eyes watering and his skin sizzling. He, too, began to scream.**

**Carnivora yelled, “Mooooooooom****mmmm mmmmmmyyyyyyyyyyy!” And Tarax roared. Her mother came running outside, her once-white lab coat flying behind her like wings, her long black braid trailing her like a snake. She snatched Carnivora up, yelled for Tarax to heel, and ran back into the laboratory, slamming the door behind them with a loud clang. **

**Carnivora could still hear the hiss of the airlock as it activated behind them, and the sound of the lab’s atmospherics pumping away, keeping them safe. **

**“We’ll wait here until it’s over,” her mother panted, holding Carnivora close and stroking her hair. Tarax bristled and growled low in her throat, pacing by the door like a sentry, but they could no longer hear the screams and the terrible coughing coming from the garden.**

**9/29/15: Today we had the protagonists meet at last!**

**10/6/15: Today we entered Dr. Moonflower's evil lair, and his two henchmen are in big trouble for losing Carnivora.**

**10/13/15: Today we helped Dr. Moonflower poison Mr. Mazulee. **

**10/20/15: Today we helped Dr. Moonflower TRY to poison Mr. Manchineel.**

**11/3/15: Today we refined some of our descriptions of our two villains and worked to make them distinct. We are sill in the scene where Dr. Moonflower tried to poison Mr. Manchineel with moonflower vines and spiky seed pods, and Mr. Manchineel fought back with a flaming mouthful of poisonous manchineel apple.**

**11/10/15: Today we returned to Carnivora and Minke, up in the canopy of the rainforest. We're trying to figure out what Carnivora wants, and we also discussed the flaws both of these characters will need to overcome.**

## Extended Learning Opportunities:

**Week 9:** Try out some numbers to find their FACTORS, and make the RECTANGLES. Which are PRIMES? Which are SQUARES? Which are NEITHER? What are the multiples of these numbers? Which "factory workers" work in the FACTORy that makes this PRODUCT?

**Week 1:** Keep puzzling with the 4 Fours

**Week 2:** Play Tic Tac Trouble and bring it back. Fibonacci puzzling. 100's chart ideas. Keep looking at Number Visuals

**Week 3:** Keep puzzling with the Fibonacci pattern; Try to unlock the Function Machine; Look at the results from the Cogs exercise and see if you have any hypotheses.

**Week 4: **Come up with a function machine challenge to share. Try some of the Wheel Shop beyond Level A. Each level gets harder, and I DON'T expect you to do more than is a fun challenge.

**Week 5: **Play with Google Draw and be ready to SHOW your soluitions for The Wheel Shop A and B (we did not return to this project and we're letting it go).

**Week 6:** Design a Function Machine to Share with the group

**Week 7**: Play with the binary dots, practicing translating numbers from base ten to base two.

**Week 8: **Do what you can with the paper I sent home about SQUARE numbers, CUBED numbers and PRIME numbers. Look to the right to see the questions I sent!

FIRST TWO WEEKS:

Through a rotation of all the students—so that they get to know all the teachers and one another and so that we get to know them—I will be getting a sample of where each child is as a burgeoning writer and storyteller.

I will be helping the kids get to know one another through their stories, while teaching them a simple way to plan, share, and write (in whatever way they currently write) the story down. It's fun! For more information, see DEB'S WRITING RESOURCES to learn more about Small Moment Stories.

# URCHINS 2015-2016

## Tuesday Sea Urchins

Second Semester Writing Focus Group:

Code Breakers

THIS FOCUS GROUP BEGINS at 9:40 and GOES UNTIL 10:30. PLEASE BE ON TIME!

This group will tackle the world of decoding and encoding. We will play with different kids of codes (whole word) and ciphers (letter by letter).

5/17/16 **DAY 15: **We completed (running out of time!) our allegory called The Planet Tree

5/10/16 **DAY 14: **We used Storybird.com to begin a story called The Planet Tree.

5/3/16 **DAY 13: **We did another Making Words activity (the final word was PLANETS which gave us the SEED for our final story)

4/26/16 **DAY 12: **We did a Making Words activity (the final word was ELEVATOR).

4/19/16 **DAY 11: **We created a post-it scavenger hunt for the Monday Squirts.

4/12/16 **DAY 10: **We created a story using the Once Upon a Time Fairy Tale cards.

3/29/16 **DAY 9: **We continued to learn about how to code the vowel sound of each syllable with the breve and the macron, and we practiced breaking the Urchin names into syllables to code the vowel sounds for open and closed syllables!

3/22/16 **DAY 8: **We began to learn a coding system for the VOWEL SOUNDS of ENGLISH! We practiced with some simple words.

3/15/16 **DAY 7: **We made our own crossword puzzles using the names of the Urchin students!

3/8/16 **DAY 6: **We completed our crossword puzzle of the symphony instruments.

3/1/16 **SYMPHONY and WETLANDS trip.**

2/23/16 **DAY 5: **The kids used the Rosecrucian cipher to reveal the names of orchestra instruments from the STRING section, the BRASS section, the WOODWINDS and PERCUSSION. We started an instrument crossword puzzle.

2/16/16 **DAY 4: **The kids looked at the Rosecrucian cipher, figured it out, and used it to find clues for a "post-it scavenger hunt."

2/9/16 **DAY 3: **We played with the Caesar Cipher Disc to decode our secret messages as the spy in Czechoslovakia.

2/2/16 **DAY 2: **We played with the Caesar Cipher Disc to encode secret messages for our spy in Czechoslovakia.

1/26/16 **DAY 1: **We played with the Caesar Cipher Disc to encode and decode, starting with our names. We also played with making words from the letters of our names and figuring out what things we could make by combining two names.

First Semester Math Focus Group:

Math Puzzlers

THIS FOCUS GROUP BEGINS at 9:40 and GOES UNTIL 10:40. PLEASE BE ON TIME!

This group will tackle good, juicy, HARD problems and puzzles. We will focus on the Math Practice Standards, especially the first four:

1. Make Sense of Problems and Persevere in Solving Them

2. Reason Abstractly and Quantitatively

3. Construct Viable Arguments and Critique the Reasoning of Others

4. Model with Mathematics

1/5/15 **DAY 13: **We played a game called Strike It Out where the kids derived the rules from the first three turns, and I sent home a puzzle called What's The Secret Code that should be a good challenge.

12/15/15 **DAY 12: **We reviewed the homework page about dividing 24 brownies equally among FIVE people, and determined that getting four and four-fifths brownies was MORE than 4½ brownies! We played Match My Part (and caused some moments of "hnnnh?" and some of "ah-ha!" It's an introduction to some pretty fabulous connections...

Here's a game that does some of the same practice, but doesn't really teach the WHY.

This one SHOWS **equivalent fractions**. This one SHOWS the comparison of **fraction and percent**. This one SHOWS the comparison of **fraction and decimal**.

This one models what the fraction (PART OVER WHOLE or how many of the fraction-sized pieces do we have? For example, if I have three of the five pieces, I have three fifths). This game will SHOW how the fraction and percent are related on both a circle graph and a bar graph! Another resource.

12/8/15 **DAY 11: **

We reviewed the Cube Brain Teaser home extension activity and played ADD IT UP. We also played How Close to 100.

12/1/15 **DAY 10:**

We reviewed the ideas of CUBES, PRODUCTS, FACTORS, MULTIPLES, PRIMES, and SQUARES. We looked at creating rectangles for FACTORS over TEN using BASE TEN BLOCKS (which will lead into binomial factoring!!!) We played ADD IT UP. We also played How Close to 100.

11/24/15 **DAY 9:**

We checked in about the page I sent home last week about Prime numbers, Square numbers, and Cubed numbers, to see how much sense it made or didn't make... We talked about growing our brains (literally) through the struggle to understand or learn something new, how it grows synapses from mistakes, and how we myelinate those neural pathways through practice. I let them know that reason I send "homework" home is to help them keep myelinating their synapses.

We reviewed the idea that all rectangles have four right angles, and two sets of parallel sides. We confirmed that **a square is a rectangle** where all four sides are of equal length.

We investigated that multiplication makes a number over and over, say the number six, four times, which is also the number four, six times. The total (in this case, 24) is called the PRODUCT. The numbers we make and the number of times we make it are called the FACTORS.

If we build that number (the PRODUCT) by making RECTANGLES with square tiles, we can find out what numbers (the FACTORS) we can multiply to get a particular number. We SAW which are PRIME NUMBERS and which are SQUARE NUMBERS.

Here's the idea. If I make the number ONE with square tiles, well, I only have ONE tile. The sides are both 1. I make 1 ONE time. The only "rectangle" I can make is the square made of ONE tile:

Because it only makes one rectangle (which, in this case, is a SQUARE), it is a PRIME number.

Because it makes a SQUARE rectangle (all sides are EQUAL length), it is also a SQUARE number.

The multiplication problem is 1 x 1 = 1. The PRODUCT is ONE and both of the FACTORS are ONE.

SO, what if we make the number TWO?

We start with TWO square tiles and see how many rectangles we can make.

We can only make **this** rectangle with an area of TWO tiles. We can rotate it, but it will always have one side that is 1 and one side that is 2. It makes only one rectangle, and one side of the rectangle is ONE (the other is the number we made). It is a PRIME number. We can't make a SQUARE. It is NOT a SQUARE number (all sides are NOT equal). The multiplication problem is 1 x 2. The **FACTORS** of the **PRODUCT** 2 are 1 and 2.

We reviewed our investigation of numbers up to NINE tiles, and we recorded how many rectangles (including squares) we could make with each number. We found the multiplication problems, noticed which were** SQUARE** numbers, and which were** PRIME** numbers (only can make a single rectangle with one side ONE tile high and with a width that is as long as the number of tiles we are using—the number we made).

Prime numbers make rectangles that are all sort of **long and skinny** (except the number one, which makes a square). ALL numbers can make a long skinny rectangle like this (1 x the number = the number, because we make the number ONE time). **PRIME numbers can ONLY make a long skinny rectangle (except for 1 which is prime AND square).**

**Here's what we found:**

**THREE:**

1 x 3 = 3

**FOUR:**

1 x 4 = 4

2 x 2 = 4

**FIVE: **

1 x 5 = 5

**SIX:**

1 x 6 = 6

2 x 3 = 6

Of these, (the numbers 3-6), any that have **ONLY ONE** rectangle (long and thin, with one side that is 1 long and the other side that is that number long) are **PRIME**.

Of these, (the numbers 3-6), only ONE is a **SQUARE** number. Is this square number also PRIME? What number was squared to make this square?

What will the NEXT square number be? What will the NEXT prime number be? What will the next number be that is NEITHER square NOR prime? How do you know?

We investigated the numbers 23, 24, and saw that 25 is a SQUARE. Try some other numbers at home!

11/17/15 **DAY 8:**

We played Add it Up. We made square numbers and cubed numbers, and began to investigate prime numbers.

11/10/15 **DAY 7:**We talked about exponents, figuring out powers of 2, and then played with making numbers in binary. We learned that any number to the zero power = 1, and explored why that works. We calculated up to 2 to the eleventh power! Binary Dots

11/3/15 **DAY 6:**

We did a quick Function Machine (first, x + 3, then 2x + 1; Both began with input of 2 and output of 5) played Place Your Number Value and Add it Up. Bring a Function Machine to share next week!

2 |
5 |

6 |
13 |

0 |
1 |

10/27/15 **DAY 5:**

We looked at True or False equivalencies to SEE the underlying patterns. We mostly looked at the one in orange, to see the pattern of doubling and halving, at the one in green to see that I simply moved 20 from the first addend to the second, and at the one in aqua to learn about parent

heses and to see the distributive property.

I also showed (very quickly) a little about Google Draw and how we can SHOW our thinking and our proof with a model, which we will look at next week.

10/20/15 **DAY 4:**

Graph the function machine and see if that helps us figure it out (slope, linear equations...)..

Look at the Making Tens Number Talk

Begin the Wheel Shop Problem of the Month NOTE: Each level gets harder. I expect kids to STOP when it's not fun!

FUNCTION MACHINE GRAPH:

**Function Machine**: This is a TWO STEP machine.

The SAME TWO THINGS happen to every number that goes in to get the number that comes out. This one was tricky!

__IN OUT__

5 7 ½

6 9

1 1 ½

2 3

8 12

**Wheel Shop Problem: **

Level A is designed to be accessible to all students and especially the key challenge for grades K--1.

Level A will be challenging for most second and third graders.

Level B may be the limit of where fourth and fifth grade students have success and understanding.

Level C may stretch sixth and seventh grade students.

Level D may challenge most eighth and ninth grade students, and

Level E should be challenging for most high school students.

These grade-level expectation are just estimates and should not be used as an absolute minimum expectation or maximum limitation for students.

Problem solving is a learned-skill, and students may need many experiences to develop their reasoning skills, approaches, strategies, and the perseverance to be successful.

The Problem of the Month builds on sequential levels of understanding. All students should experience Level A and then move through the tasks in order to go as deeply as they can into the problem.

**Overview: In the Problem of the Month The Wheel Shop: **

Students use algebraic thinking to solve problems involving solving for unknowns, equations, and simultaneous constraints. The mathematical topics that underlie this POM are variables, inverse operations, equations, equalities, inequalities, and simultaneous systems.

In the first levels of the POM, students are presented with the task of considering a tricycle shop with 18 wheels and asked how many tricycles there are. Their task involves finding an unknown and "undoing" the straightforward question of how many wheels 6 tricycles have in all. As one continues through the levels, students are presented with situations that involve components of bicycles, tricycles, tandem bicycles, and go-carts.

These situations can be translated into systems of constraints with equal numbers of unknowns. Students are asked to define the relationship between two unknowns. In the final level, students are presented with a logic situation that involves using rational numbers, inequalities, and a set of constraints. Students are asked to find the number of bikes in the shop and the range of repairs that need to be made.

10/13/15 **DAY 3:**

We re-posted the **Fibonacci** numbers to keep pondering: 0, 1, 1, 2, 3, 5, 8, 13, 21

WHAT'S THE PATTERN?

**Function Machine**: This is a TWO STEP machine.

The SAME TWO THINGS happen to every number that goes in to get the number that comes out. This one was tricky!

__IN OUT__

5 7 ½

6 9

1 1 ½

2 3

8 12

We did two **Number Talks:**

**Number Talk: 48 **

**(what are some ways to make this number?)**

6 x 8

8 x 6

96 / 2

4800/1000

480 / 10

48 x 1

12 x 4

24 x 2

24 + 24

4! + 4!

2(4!)

5 + 25 - 2

40 + 8

(4 x 10 )+ 8

100-50-2

**Number Talk: 5 + 8 + 7 **

DECOMPOSING NUMBERS

How did you think about it? Can you think of more ways to solve it? Can you DECOMPOSE each number to make tens with the remaining numbers?:

Decompose 5 into 2 and 3; 2 + 8 = 10 and 3 + 7 = 10 — (2+3) + 8 + 7 = (2 + 8) + (3 + 7)

Decompose 8 into 5 and 3; 5 + 5 = 10 and 3 + 7 = 10 — 5 + (5 + 3) + 7 = (5 + 5) + (3 + 7)

Decompose 7 into 5 and 2; 5 + 5 = 10 and 2 + 8 = 10 — 5 + 8 + (5 + 2) = (5 + 5) + (8 + 2)

Swish flip, rotate, and stack game

We looked at Counting Cogs We will be looking at numbers as visual puzzles and relationships.

COUNTING COGS: These seemed to work: 8 and 11; 5 and 12; 8 and 7; 5 and 8; 9 and 5; 5 and 7; 6 and 11; 6 and 7; 5 and 9; 9 and 8

These DID NOT seem to work: 6 and 8; 4 and 8; 10 and 12;

We haven't seen what's going on here yet!n

**This problem requires children to think about factors and multiples and, in particular, common factors, but it is not necessary for them to have met this term prior to having a go at the task. It offers opportunities for pupils to ask their own questions, find examples, make conjectures and begin to generalise. The problem lends itself to collaborative working, both for children who are inexperienced at working in a group and children who are used to working in this way. By working together on this problem, the task is shared and therefore becomes more manageable than if working alone.**

10/6/15 **DAY 2:**

We tried a visual representation of the numbers 1-35 and began looking for patterns in the art and in the numbers. It was a hit for some, and a miss for others! We also posed the challenge to try to figure out the math behind the **Fibonacci sequence.** I gave them 0, 1, 1, 2, 3, 5, 8, 13, 21, 33...). PLEASE DON'T TELL them how it works if you know. I want them to ponder and think about it, to try to savor the moment they figure it out. After that, we'll look into it and have more fun! Next week we'll play a game with gears, and we may try some group logic puzzles. Number Visuals. **Extended Learning Opportunity** at home will be to continue with the Number Visuals and to take home and play a word problem game.

NUMBER VISUALS

1. Write the number that each visual represents on your number visuals handout.

2. What do you see in the number visuals? Do you notice anything interesting about the way numbers are shown? Share your findings with your group members and discuss them together.

3. Look for interesting patterns. You may find it useful to use colors to highlight them. Describe some of your findings and share with your group members.

**In this lesson we share a really cool and different way of looking at numbers, which will help students see factors and multiples. Students are invited to look for patterns and to color code and ask their own questions about the interesting representations. This lesson created “oohs” and “aahs” throughout the room in our trial – students were fascinated by the numerical relationships they saw, often for the first time.**

**In the extension activities investigating consecutive numbers students can receive opportunities to understand the meaning of algebraic expressions.**

**Content:** Factors, multiples, prime numbers, number relationships, algebraic expressions and equations.

**Practices:** **MP7:** Look for and make use of structure

**MP8:** Look for and express regularity in repeated reasoning

9/29/15 **DAY 1: **We started with a math challenge using the number 4, four times in different

combinations to make the numbers 1-20... here's a link to the lesson

The kids played with ways to use the number four EXACTLY four times to make the number 1. Some moved on to try to find solutions resulting in 2 & 3.

For extended learning opportunities, they can keep going.

Some solutions for the numbers 0-20 can be found below.... Don't look until you've tried!

Some of the kids investigated the math operation with 4 called a factorial (4!). Some pondered √4. Mostly, it was a combination of = - ÷ x, including using the fraction bar as division!

Here's a snapshot of some of the crazy ways to make 1 with 4 fours:

(4÷4) x (4÷4) = 1

(4÷4) ÷ (4÷4) = 1

(4+4) ÷ (4+4) = 1

4/4 + 4 - 4 = 1

4/4 ÷ 4/4 = 1

(4!/4 - 4) ÷ √4

Don't look at the solutions below until you've played with your own!

Here's a list of possible solutions: