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Thursday, February 25, 2016

Where's the math? Differentiating Math Instruction

I purchased a fun new book last week called Math Potatoes by Greg Tang.


The book has a lot of different math riddles about grouping numbers. The riddles in the book are a little too challenging for my first graders. They are not ready for them, yet, but will be soon:)

I did, however, get an idea while reading through the book that turned out to be perfect for my class. I decided to use the very 'mathy' pictures in the book to engage my class in some differentiated warm-ups as part of our Math Workshop. I chose an engaging picture from the book and we spent our warm up time (10-15 minutes) over two days finding the math within the picture.

On day 1, I showed the picture to my students. We noticed the details of the picture and I asked them to generate some questions that could be answered using the picture. Their questions surprised me! They asked questions that were varied and rigorous.





As you can see, the level of questioning is quite differentiated. Some questions provided review for concepts already taught, some related to exactly what we are learning now, and some extended beyond the required first grade curriculum.

On day 2, I asked students to choose a question that was not too easy and not to hard for them. A question that would stretch their brain without making them frustrated. (Learning within their zone of proximal development., Vygotsky) Some students do this very well, others,  choose something fast and easy. We're working on that!

After choosing a question, students were to plan a strategy and answer the question.

Once students got started, I observed to see which students were struggling and I partnered them up with someone else who chose the same problem. This seemed to work well and freed me up to quickly confer with multiple students.

This student chose to show the combinations to 10. I was concerned because I though this was not particularly challenging for him but then I noticed he was recording number sentences with both 2 and 3 addends.

This student wanted to add the value of all the cards in each suit. She didn't finish all four suits but the work she showed on the 'hearts' demonstrates that she recognized 'friendly 10s' and was able to show expanded form for the number 14 making the mental math of 10+10+10+4 doable. 

This student's work illustrates mastery of a grouping/counting by 5's strategy. She doubled the 3 groups of 5 creating 6 groups in order to double the number of cards in the picture.

This student wanted to know how many of each card in the picture, frequency. She created a table of sorts. Her work tells me that she just needs a quick mini-lesson on structuring a frequency table...the concept is there:)

 The t-chart show that this student knows even and odd numbers...probably not so challenging for her so I might suggest a more fitting math question for her the next time.

This student created a table to show how many of each suit were in the picture then added the numbers to check that the total was 15 cards.

This student was attempting to find the total value of each group. What is interesting is that he was trying to break the addition down into manageable pieces but was 'readding' numbers (ex: used the 5 to add 4+5 then again to add 5+6) Somehow he managed to answer correctly. (?) His very organized and clear work allowed me to see his thinking and follow up with a mini-lesson on how to use this strategy correctly - and also utilize 'friendly 10s'. 


Here are some examples of other work prompted by another picture from the book.




Creating a bar graph...not an easy task for first graders! Well done:)
This piece shows total, 10 more and 10 less and correct use of <.
I'm wondering if this student counted or really added 8+9+8+5??

If you look at the picture carefully, the socks are grouped in 5's if you're grouping vertically rather then horizontally.

Clear labeling and organized work helps me see the thinking.

When conferring with this student, I asked if she knew what 16+14 was. She said 30 because 10+10 is 20 and 6+4 is 10 and together that makes 30. #tenness!


I am really enjoying this book and the way it is helping my students think about numbers and math. Additionally, it is helping me do quick formative assessments and clear up misconceptions. My students are very engaged and because it is differentiated and there is student choice, there isn't a 'bored' body in the room!


Thursday, February 18, 2016

Where's the Engineering: Wild Feet

Our latest engineering challenge, Wild Feet, was centered around the idea of biomimicry. Scholars were introduced to the idea that engineers often look to nature to solve problems. In this particular challenge scholars were asked to work with a partner to investigate materials then plan and design a model of a shoe sole that would not slip or slide easily.
We first examined several different animal feet to observe how the unique structure of their feet helped them survive in their habitats. (This idea is part of an upcoming science unit and this challenge laid the groundwork for our study of animal characteristics and adaptations.)


The next step was to investigate some of the design materials that would be available. Scholars investigated the properties of the materials as well as how the individual materials performed on the testing surfaces. 



Scholars then used that information to work with a partner to create a plan that would guild them through the design process.





The plans were then used to design the sole for the shoes.



 


Scholars then tested the soles on rough and smooth surfaces and on gentle and steep inclines.

After much testing...and predicting...and discussion...and improving... scholars concluded that rubber, ridged weather stripping placed horizontally, created the best non-slip sole for a shoe.


So, what important engineering concepts were learned?
  • Engineers sometimes look to nature to solve problems.
  • Investigating materials prior to planning is an important step in the engineering process.
  • Paying attention to data gathered during investigations leads to effective planning.
  • Sharing ideas and listening to ideas within a partnership is important.
  • Precise and thoughtful building/designing leads to successful models.
  • Gathering information during the testing phase of the engineering process is critical before planning improvements.
  • Modesty in success and persistence in trial are important character qualities.