Logic Puzzles (1-2) (3-5) (6-8)

Okay, I admit, logic puzzles aren't exactly math lab in its purest form, but they're still cool. Even the 1st and 2nd graders got a taste in their math block. No writing, no predicting, no investigative questions, just x's and dots and pure 100% logic.

Binary Birthday Bracelets (3-5) (6-8)

Blog by Ashlee

Introduction: We are looking at another numbering system. We have a base 10 system. That means we have 10 numbers in our system. We looked at a base 5 system. But, our main focus is a base 2 system, which is called binary.

Birth date code: 

1 = dark blue beads

0 = lavender beads

Dividers = black beads

Teacher note: We used our birthday information in the form of MM/DD/YYYY then converted each of the three numbers to binary. Different color beads were used to represent 1's, 0's, and dividers. 

Spoons (3-5)

Blog brought to you by Julia

We are making boats and seeing how many spoons will fit in it. Then we have a plastic tub with water in it. We are going to put metal spoons in our boat (made of one sheet of 30 cm x 30 cm aluminum foil) and see if it sinks or floats.

My prediction is 19. I changed my prediction to 23 because of my friend. I changed my prediction again to 63 because of my friend. I got 38.

Floating Bears (6-8)

Blog entry brought you by Sasha:

We got a 30 cm x 30 cm foot of aluminum foil and tried to make a rectangular boat that will hold the most plastic bears. The point of this is to see what ratio of height to width to length will be the best at holding plastic bears.

Prediction: My prediction is that the sides should be an inch tall and that it should be 3/4 as wide as it is long. I think it will hold about 40 bears.

Assumptions:
- Everyone uses a 30 x 30 x 30 cm piece of foil
- All sides must be square (rectangular)
- Only use big bears

Boat Dimensions:
height = 5 cm
length = 22 cm
width = 22 cm
volume = 2420 cm3

Based on Emma's, I'm changing my prediction to 150.

Results: It held 209 bears and 25 spoons.

Experiment #2 (try 2)

We're not going to use bears anymore, because they're too light. We're going to rebuild our boats and only use spoons.

Boat #2 Dimensions:
length = 17 cm
width = 17 cm
height = 7 cm
volume = 2023 cm3

I made the sides higher because the last one sank because the water went over the sides.

Prediction: I predict it will hold 60 spoons.

"We've used ALL the bear counters. What do we do now?"

Volcano (6-8)

"Introduction: There was a video in which a volcano goes off. In the scale, it moves 1 cm per hour. There is a map with the same volcano and same scale with a lot of cities." - A.K.

This is a Dan Meyer 3-Act Play: http://www.101qs.com/3542

Assumptions:
- The lava moves at the same rate.
- We'll measure the city at its center.

 Some questions we have chosen to investigate:
- What is the order that the lava will reach the cities?
- Is the lava increasing at a constant area or distance from the center of the volcano?
- How long will it take to reach the first city?
- How much area will be covered by the lava after _____ seconds or minutes?

This is part 1 of 2 and will require another lab day to complete our investigations.

Pizza Choice (3-5)

We have a real problem to solve today! Mrs. Korytko has commissioned us to poll the school and ask for their favorite pizza toppings. We will collect the data and decide on the best way to represent the information to help Mrs. Korytko plan her pizzas. Then we will make recommendations to Mrs. Korytko about how many of each pizza she might want to make (using the ratios we created).

Assumptions:
1) We can only survey people who will be at our school on Friday.
2) We will offer the following choices:
- meat only
- cheese only
- veggies only
- meat and cheese
- meat and veggies
- cheese and veggies
- meat, cheese, and veggies

Angry Ducks (3-5) (6-8)

Goal: To design and construct a rubber ducky launcher that can land in a giant IKEA leaf from 4 meters away. 

1) draw the design

2) construct the launcher

3) test the launcher

4) record the results of the trials

5) adjust based on results

We LOVE failure. When we fail and adjust, we act like scientists. 

The upper graders met and agreed on rules to make things fair: 

1) You must only use the materials given, but you do not need to use all the materials.

2) You may use your own strength to pull the ducky back, but you may not use your strength 

3) You are allowed 3 trials.

4) The launcher must be able to be used multiple times.

5) No ducks may be harmed in the process (no cutting the heads off the ducks). 

When you adjust your design, leave the original design in your lab. Don't cross it off, don't erase it, leave it. Write about how you changed your design so others can learn from your failures and adjustments. 

Diggers (3-5)

This problem is based on Dan Meyer's 3 Act Play called Ditch Diggers. In the video, you  have to predict whether or not the ditch diggers will meet, and if so, on what day. In Act 2, coordinates are provided, and in Act 3, the solution is shown. We are using revised problems with the following coordinates.

SCENARIO 1:

Digger A (Let's call him Albert)
day 0 (0, 0)
day 1 (1, 1)
day 2 (2, 2)
day 3 (3, 3)
day 4
day 5...

Digger B: (Let's call him Barney)
day 0 (19, 36)
day 1 (18, 33)
day 2 (17, 30)
day 3 (16, 27)
day 4
day 5...


SCENARIO 2:

Digger C: (Let's call him Clyde)
day 0 (2, 1)
day 1 (4, 5)
day 2 (6, 9)
day 3 (8, 13)
day 4
day 5...

Digger D: (Let's call him Daryl)
day 0 (22, 38)
day 1 (21, 36)
day 2 (20, 34)
day 3 (19, 32)
day 4
day 5...

Our questions are:
- Will the diggers meet in each scenario?
- If they meet, on which day?
- If they don't meet, who should adjust and on which day?

Our assumptions are:
- The diggers keep the same rate (or slope) each day.
- The diggers don't stop for weekends and holidays!

Mystery Blocks (6-8)

More blocks. This time with 45% more work with percents and probability! Math Lab with the upper graders usually takes 2 math periods a week (with accelerated old-school book and paper work the other two days). This means we have more time to go greater in depth. Day 1 was pretty fun and included some jumping cheers when predictions were correct. I have some great pictures of the excitement, but we always ask for parents' permission to publish images of their children. Today they were told EVERYbody gets their writing on the blog, and I saw a huge improvement in length of writing and inclusion of some math thoughts. They have a real audience! 

Solution: 5 tan, 2 blue, 3 yellow 

Tomorrow we'll graph the results on a bar graph and learn how to convert percents to degrees to make an accurate pie chart using the real ratio.