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Counting All The Things (K-12) [video]

Montse Cordero — Fri, 15 May 2020 03:53:47 +0000

In this activity explore ways of counting large amounts of flowers, trees, birds, people, and more in spaces and places you go. While you’re out for a walk in the neighborhood or making a run to the grocery store take a picture of a crowded flower patch or bread aisle and discuss ways of counting how many flowers or loaves of bread there are.

Print the picture, annotate it using any image editing software available to you, or upload it to Geogebra to use the grid lines and their other tools. Think about different ways of counting and representing your thinking visually. If you want to explore with algebra ask yourself questions like, if my bedroom floor was covered in flowers like this flower patch, how many flowers would it take? Consider modeling your thinking about questions like this using algebra and generalizing it for any space.

You can also find a version of this in Mathematical Mindset Book 4, How Crowded is the Crowd.

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Jumbled Hopscotch (2-12) [video]

Montse Cordero — Fri, 15 May 2020 00:39:41 +0000

Lately, we’ve seen some lovely hopscotches made by our neighbors in sidewalk chalk for everyone to use, but what would happen if we jumbled the numbers? First, we can ask ourselves: How many ways can we reorganize the numbers in hopscotch? This can be a tough question, so we might want to start with a hopscotch that goes up to 4 or so and then follow the pattern from there. But we can also wonder: Out of all the ways of reorganizing the numbers, how many can we still jump through? If the 1 is too far from the 2, it might not work out! What does this depend on? How many jumpable hopscotches can you make?

Jumbled or not, you can still ask other hopscotch questions, such as: If you add up every number you hopped on, how many ways can you jump through your hopscotch such that your numbers add up to 15? How many different totals can you make? Are there totals that are impossible to make? What about ones that come up a lot? Your answers might be different depending on how jumbled your hopscotch is!

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Number Hunt (K-8) [video]

Montse Cordero — Fri, 15 May 2020 00:36:00 +0000

In this activity, students guess the number you are thinking of given clues. This is a fun way to build number sense, logical reasoning, and mathematical vocabulary. If students can’t remember some of the vocabulary or concepts, it is a great opportunity to have some conversations about them. It can be useful to let kids use a hundred chart to keep track of which number it is not. Ask your student why they are crossing out certain numbers and not others. This activity comes from books by Terry Kawas.

Here is a hundreds chart: https://www.ccboe.com/schools/jenifer/images/pdfs/100Chart.pdf

Example 1

The number is greater than the number of pennies in a quarter
The number is less than the number of pennies in five dimes
The number is an odd number
If you count by 5’s you say the number.
The sum of the digits is 8.
What is my number?

Example 2

It’s more than 43.
It’s less than 50.
It’s an even number.
Both digits are the same.
What is my number?

Example 3

The number is greater than 6 x 4.
The number is less than 8 x 7.
The number is even.
The number is a multiple of 3.
The difference of the digits is four.
What is my number?

For older grades, students can make their own number hunt.

You can adapt this for younger grades by using different vocabulary appropriate for their grade level or using the numbers 0-10. For example, for kindergarten, you could have them draw the numbers from 0-10 on a number line. They can guess a number and you can tell them it is bigger or smaller than that number. With each guess, they can narrow down which numbers it could be.

You can find more of these problems in Terry Kawas’ books here: http://mathwire.com/problemsolving/guessthenumber.pdf and http://mathwire.com/hblogic/hblogic2.pdf

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Reduce, Reuse, Geometry (3-12) [video]

Montse Cordero — Fri, 15 May 2020 00:35:17 +0000

Intersecting a 3D shape and a plane might seem intimidating, but a few bottles, a box cutter, and some creativity can give us some insight into what it can look like. A particularly interesting 3D shape to cut is the cone, as depending on how we cut, we can get circles, ellipses, and parabolas (hyperbolas too, those are harder to cut out). Thankfully many bottles include cones, so we can have some fun cutting up bottles and using the conic sections we get to make art. Watch the video below for more details and some examples!

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Apple Orchard (4-12) [video]

Montse Cordero — Fri, 08 May 2020 03:20:01 +0000

This layout based on how apple trees are planted in orchards leads to some interesting explorations of area, patterns, and growth rates. Younger students can model the situation with beads or beans, while older students can graph the growth rates they find. Watch the video below for the pattern (also included in the lesson linked below) and more details!

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How Tall Is That Tree? (2-12) [video]

Montse Cordero — Fri, 08 May 2020 03:19:12 +0000

How many times have you come across a tree and thought that tree is humongous? What do you measure with? Considering I usually don’t carry measuring tools on a walk or hike I’m often puzzled by how I could get the most accurate measurement of the tree especially since the tree would be way too hard to measure. I start wondering what I know the height of and if I could use that to get a good estimate of the tree’s height. Try it when you’re outside with family and friends. Challenge each other to come up with multiple strategies or being as accurate as possible to determine the height of the trees you’re curious about.

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Pixel Art on Windows (K-12) [video]

Montse Cordero — Thu, 07 May 2020 23:02:53 +0000

We’ve been inspired by the beautiful art many people are making on their windows with sticky notes to cheer up their neighbors as those are pixel art, and we had written a lesson for the classroom around that idea! You can use sticky notes on a window or wall to make a design. Lots of math can be involved in the design, and later you can ask the questions we asked in our pixel art lesson but applied to your own piece!

As you’re making your piece:

Design it on grid paper or pixel art software (such as https://www.pixilart.com/draw).
How many sticky notes of each color will you need?
How can you know how much wall/window space you will need to put up your design?
Or going the other way around: measure the wall/window you want to use and decide how many pixels wide/tall your design can be.

Once you’ve made it:

Pick one of the colors you used. Your challenge is to cover all the pixels of that color using rectangles. Your score will be the area of all the rectangles used plus the square of the number of rectangles. Try to get the lowest score possible! (See the lesson plans or video below for more details.)

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Fraction Hunt (2-8) [video]

Montse Cordero — Thu, 07 May 2020 22:53:32 +0000

Fractions are all around us! Walk around the house, yard and neighborhood with your child. Where do you see fractions? What would you call one part of the whole? For example, one rectangular stepping stone of 13 equally sized stepping stones would be 1/13th of the stepping stones. What if the objects are different sizes? Can they still be represented as a fraction? In the video, Kate represents one black key on the piano as one out of the total number of black keys. However, one white key can’t be represented as a fraction of all of the white keys since they are different sizes. Can you represent the object in more than one way? For example ⅕ is equivalent to 2/10. Can you see this in the object?
This activity is inspired by Mindset Mathematics Curriculum, Book 3, I spy 1/2.

Extensions:

- Draw shapes on the sidewalk in chalk. Split the shape in half and shade half, name the fraction you see. Split the shape in half again, making fourths. What would you call the colored portion now? Write an equivalence statement. (½ = 2/4) Can you make more? Make art on the sidewalk and have conversations about the fractions you see in the art (https://www.youcubed.org/resources/sidewalk-chalk-designs-k-12-video/). What fraction are each shape of the whole? What other fractions have you made?
- Finding ½ in an art piece. In this piece of art below, highlight where you see ½.

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