Saturday, September 27, 2014

Guest blogger from digiblock.com: place value and division

I'm happy to welcome fellow teacher Avery Stern at Digi Block. She has some fall activities and great division tips as you teach your students!

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What’s More American Than Apple Pie and Fair Shares?

In the words of a soft-rock singer “When autumn comes, it doesn’t ask, it just walks in where it left you last,” and autumn, has marched right in with all things pumpkin, apple, knitted, and spooky. It can also be a time for classroom cooking and group activities - so what better time that to start introducing the daunting division unit than through fun, autumnal themed lessons?

One of the things we really like to emphasize here at Digi-Block is the idea of self-discovery. A way of increasing the likelihood of student engagement and excitement is by introducing this lesson without even whispering the D word; Donuts? Dragon-tales? Dasypoedes? Division.

To young students, division can often seem like the no-good-very-bad-fourth brother of math...But I quite like division...and it’s an undeniably necessary skill. So let’s teach that D word in the most useful way possible - real life scenarios.  

Here are two, introductory activities for Secret Division using our favorite math manipulative, the Digi-Block!

Dividing the Pie


In this activity students will:


  • Use the blocks to determine how to make fair shares of a known quantity                                                                   

  • Materials: Digi-Block of 1000, or other manipulative ie. pennies, counters, etc. and worksheet

Introduction: You’ve gone apple or pumpkin, or nose picking; let’s use Digi-Blocks to develop a fundamental understanding of “giving everyone a fair share.”


Instruction: Say you have 15 students in a class, and you’ve picked 240 apples - We’ll use Digi-Blocks as our rot-free substitute. How neat and clean! ... Like our hands before we start dolling out ripe produce.

Have your students predict how many apples, (pumpkins, boogers, or blocks), each child will get depending on the amount they collect.

Have your students brainstorm how to equally distribute the goods. They may start by handing each person one at a time. Thats OKAY! Let them tediously work out the problem.

Now have students pack the blocks into tens and hundreds.

Questions to Ask:

Can each student receive a full block of 100?

Can each student receive a block of 10?

How many single blocks will each student receive?


Were there any leftovers?

Did you have to unpack the blocks to fairly distribute them?

Do you think there are times we won’t be able to fairly distribute the apples? (If students are at a point of extended thinking)
ex answer: “When we change the number of apples or we change the number of people.”

Hmmmmmm. Tricky.

Variations:
  • Try the lesson with each group using different forms of 100. Ex. Loose single blocks, tens blocks, or pre-packed 100 blocks and remainder. Have students discuss what was easier.



Ask: Why was one way easier than the other? ie. the base 10 number system bundles up units so that we don’t have to individually count.

  • give some groups apples that will equally share out and have others that will leave them with a remainder. Can students find similarities and differences in division problems that leave remainders. Do the problems out with the blocks.

Pumpkin Carving and All that Leftover Gunk:

Introducing the remainder and peaking student curiosity.  




In this activity students will:

- Learn about remainders through self-discovery and real-life problem solving.

  • Materials: Digi-Block of 1000, or other manipulative ie. pennies, counters, etc.
  • An array mat (print out attached).

Instruction: You can begin by breaking your classroom into even groups. Have your students figure out how large the groups should be as a warm-up to your division lesson.

Provide each student with an array mat, blocks, and a series of short word problems. (worksheet attached).

Ex. You are carving pumpkins for all the houses on your street. There are 7 houses and 68 pumpkins. How many pumpkins will each house get?

Lets show this with blocks.

(insert image pumpkins_packed.jpg)

Question to Ask:

“How can we use what we know to come up with an efficient, simple way, of dividing up these pumpkins/blocks?”

Remind students that packing blocks to represent pumpkins is a great place to start, and they should log their thought processes in their math journals. <-- a great way of assessing progress and deep conceptual understanding.

Students may come up with several different ways of answering the problem. Repeated subtraction*, written work, or distributing in even groups on the array mat are all great options.

Questions to ask:

After they divide, if we took all the pumpkins back, how many would we have? How can we show this with a number sentence? What does this teach us about checking your work?

*Using repeated subtraction as a method of elementary division can be a great way to start. It’s important to emphasize that repeated subtraction is the not the same as division even though repeated addition is multiplication. Can your students figure out the reason for this? Sometimes it takes adults a bit of time as well! Repeated subtraction finds the number of equal groups while sharing finds the number IN each equal group.

ex. 25-8-8-8 = 1 not the same as 25/8 BUT 8+8+8 = 24 which IS the same as 8x3

Variations:
Ask your students not only to share their discoveries, but swap technique with another group.

As for the remainder, remind your students that real-life division means there are real-life solutions to what’s leftover.

Challenge Question: What does the remainder represent and why can’t we just make another group out of it?

Even though we often ignore the remainder in a division problem - If they really did have too many pumpkins, what could they do with it?

Give them to a friend who doesn’t live on the block? Use them to decorate their own front porch? Make pancakes and pumpkin seed snacks out of them? Cut them into bits and leave it for the compost?

Peak your students’ interest. Instill curiosity!

Math is everywhere from the World Series to how many table spoons of cinnamon to toss into that delicious vat of hot cider. Maintaining a clear reminder of this is vital to a student’s engagement.

And just to top it all of, follow this lesson up with a real autumn activity like leaf collecting and dividing, pie baking where division and measurements are unavoidably enjoyable, or my personal favorite; predicting how many pieces of Halloween candy they would need to collect to have enough for a few sweet treats every week!

General Tips for when your students are stuck:

  • Simplify the problem. Focus on identifying patterns rather than getting the answer correct.
  • See if they can work backwards and find the exact point in the lesson where the challenge becomes too much.
  • Encourage self-correction by asking questions to help them identify points of error.  ie. They make an incomplete group out of the remainder. Can they workout why this isn’t a viable solution?
  • Put the blocks away and simply talk about potential solutions. Then dive back in, but slowly! Always start with an easily doable problem. This provides a confident start for students.

And most importantly:
  • Listen to some dance music. Dance to the dance music. Sing to the dance music. Boogie woogie woogie until you just can’t boogie no more.

Wow! Great info Avery! Thanks for being a guest blogger at Kids Math Teacher. If anyone wants to be a guest simply email me at kidsmathteacher@gmail.com with your guest post idea and we'll go from there. Have a great rest of your weekend!

Thursday, September 25, 2014

2nd Grade MaTh: Fall Rekenrek for 2.OA.B.2 (adding & subtracting within 20)

Hey everyone!  Just a reminder that my place value items are on sale (20% off) until tonight on Teachers Notebook, so if you haven't gotten them already, check it out.

Today for MaTh we'll make a fun fall Rekenrek to practice adding and subtracting within 20.  You can join in the linky MaTh party for a few more days (this is our last week on 2nd grade--next month 3rd).

Okay, here's some of the supplies...
 and this is what it looks like after it is put together.
Kids can decorate and put their name on their personal Rekenrek leaf.

Instructions:  Once you have assembled the Rekenrek by stringing all the beads and tying the ribbon in the back it is time to play!
  • Have students practice a few problems of their own (9+8=_, or 7 +3=_) saying it quietly to themselves.
  • Then have them practice with flash cards as a class, small groups, or individually.
Rekenreks are great because it helps the children see how single digits relate to the 5 and 10.  They can see that 8 is actually 5+3 and when they are adding another number to that, such as 3, they can visualize and move the beads to see that two more makes ten and then there is still one more bead for a total of eleven.

What kinds of activities are you doing with your students?
You can add your 2nd grade MaTh today or until the end of the month : )
See you Saturday with a special guest blog post!


Thursday, September 18, 2014

2nd Grade MaTh: CCSS 2.G.A.3 ~ partitioning shapes (equally!)

Happy Thursday!  Today for MaTh (math activity Thursday) I'm looking at CCSS 2.G.A.3 (only fitting since I did the standard 2.G.A.2 last week)

Here is what 2.G.A.3 states...
Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Sounds pretty good, but the last sentence I am not sure what they mean by that.  If you know I'd love to hear what you think.  If wholes are identical doesn't that mean they are the same shape?  Anyway, my activity is for the first sentence of this standard.


Activity Name: Partitioning shapes (equally!).  Any kids can partition shapes... Yep, drawing lines through objects is easy, but how can we make all the sections equal!?  Get out the rulers, compasses, and protractors students!  For the easy way you can fold papers, but I recommend trying the measurements too.

Concepts:  Geometry (knowing more than just the shape, but to divide up a circle we will need to know the center point and discuss degree measurements perhaps), early division (in order to make things truly equal we will be dividing a bit), and fractions (please let your students know that fractions are division problems too).

Supplies: Ruler, compass, protractor, pencil (and paper).

Time Needed: This really depends on your class.  You might want to just take one shape at a time and do one each day.  We are doing both a rectangle and a circle today.

Instructions:

  1. Have your students draw a circle with their compass (marking the center dot) and a rectangle--making sure that they have 90 degree angled corners.  (You can and should discuss this with them)

  2. Discuss partitioning.  What does it mean?  If we put three partitions in any rectangle would it make each part 1/4?  Discuss the importance of having each part be equal.
  3. Teach how to find the equal partition.  
    • With the circle, explain that a full rotation is 360 degrees.  For any line to divide the circle it needs to pass through the center point.  (challenge: if you don't know the center point you can cut out the circle and do this exercise with exact folds for halves and quarters) Drawing a line that goes through the center point will divide it in half, but when we do a second line (as to make it into 4 parts, we need to make sure that there is a 90 degree angle to ensure exact division of parts).  But what about the 1/3 of a circle?  See if the kids can figure it out or have ideas how to find 3 parts with 360 degrees.  Eventually they will discover and you can teach that each angle will need to be 120 degrees coming out from the center point.

    • With the rectangle, it is important for the kids to understand in order to make equal parts it is important to measure (or make exact folds).  With rectangles there are more ways than one to make half and a fourth (due to using vertical and horizontal lines).  It may be easiest to cut the paper out and just do folds, but it would be great for students to do the measurements and find the half-way points.

       Can the students find the half way mark?  Here, I know half of 5 is 2.5 and then I need to keep going to half 0.3 (0.15).
  4. Have kids play and discover.  The more they do these types of hands-on activities the more they can grasp other geometric concepts too!

Thursday, September 11, 2014

2nd Grade MaTh: CCSS 2.G.A.2 rough area of a rectangle

Hi!  It's Thursday so time for Math activity Thursday!

All this month has a 2nd grade focus.  Today's activity/lesson teaches CCSS.2.G.A.2 which reads...
Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
Activity Name: Squarin' Up Rectangles!
Concepts: Area, shapes, measurement--Partitioning anything into squares is really all about area.
Supplies: Easy--blank paper, ruler (recommend with cm measurement), pencil, and 2 colors (either 2 crayons or markers)
Time needed: 30 minutes for a class, but if doing at home it can be as little as 15.
Instructions:

  1. Have student hand draw a rectangle on their blank page.  You may want to remind the kids that rectangles corners are 90 degree angles (like an L shape), so when they draw their rectangle they do the best straight edges they can. (I used a pen, but students will use a pencil)
  2. Using a ruler start at one of the corners and make a mark at each centimeter. On each of the parallel sides (BTW you should use these terms with the kids--it's important to teach math vocabulary early on) make sure to start measuring at the same place.  For example, on the vertical lines I started measuring at the top and on the horizontal lines I started measuring on the left. (You could do this whole exercise with graph paper but your students wouldn't have the challenge of making a grid in their free-hand rectangle).
  3. You will probably find that not all the corners are exactly L shaped (90 degree angles) so you will need to redraw some of the sides to make them straight.  Use the ruler to draw a line between the two measured points.
  4. Explain that the columns go up and down (vertical) and rows go across, side to side (horizontal).  Most likely the rectangle will not be an an exact cm mark--just use the closest cm mark to a complete cm)
  5. Count the number of squares down each column and number them (that is how many rows there are).  In this example there are 6 squares for each column.  Kids might not be able to count by 6s (or however many rows they have with their rectangles), so we count the columns by 2s (you can count by 1s but it just takes longer and you could do 3s too).  Each time you make a slash through the blocks you write the number you are counting up to (I drew a line under each group of three numbers since that is one whole column).
    Keep going until you fill in the whole thing--finding the area inside the rectangle.
  6. Now, to double check that we did the area correctly we will also count the squares in the rows.  Label that--those are the number of columns. Mine were easy to count since there were 10 squares in each row.  Then I just skip counted ten as I marked the counting.
  7. You might want to ask the kids which way was easier for their rectangle--Counting by columns or counting by rows?  Explain to the students that they just found the area of a rectangle.  It might have been hard to do it this way, but as they progress through math their will be shortcuts to find the area.  Once they know multiplication it is just the height (vertical measurement) times the width (horizontal measurement).  In this example we had 6 rows of 10 (6 x 10) or 10 columns of 6 (10 x 6), but equal the same 60 squares.
I hope you enjoyed Squarin' Up Rectangles!

Now it is your turn to share a math activity if you want.  Here is the template and you can link up your 2nd grade activity any time this month.  In other months we will have other grades too.
I can't wait to see what kinds of activities you have!

Monday, September 8, 2014

So swamped with being busy, busy, busy!

I totally wanted to participate in the Currently linky this month but now that it is so far past the beginning of the month it kind of seems silly...

It has been majorly busy around here!  With my kids going back to school, change of tenants for the triplex we have, trying to work on my book, running critique groups for two writing groups, and just having time to keep up with laundry, dishes, cleaning, a-n-d EVERYTHING!

But it is all good!  I am feeling so blessed.  A few weeks ago I found a very plump monarch caterpillar and I took it home and that day it went into it's chrysalis.  My kids loved it! The following day I found another one and it did the same thing.  My kids jostled the butterfly house and one of the chrysalises fell.  I managed to get it back hung up with some floss and a tiny bit of super glue (but we are still waiting for that one to open--hope it's not deformed).  The caterpillar that went into metamorphosis second came out first!  It was nice enough to climb on my arm and stay for about 5 seconds before flying off.

During the last week and a half my husband and I did video for the production of The Pancake Menu--the book I will be publishing next year.  It has recipes in addition to listing the possible pancakes to order.  On the recipe page will be a QR code to go to the video tutorial on how to make the pancakes as well!  I'm super excited about it!  We did video taping over three days, (8/30, 9/1, and 9/4) to make 12 great kinds of pancakes.  I customized this apron and spatula (they will be available with imprints during the Kickstarter campaign--although they won't be hand customized : ).

What has everyone else been up to?  Has it been super hectic?
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