Sunday, August 14, 2016

Block blobs redux

Last December, we played Block Blobs (notes here). This week, we are trying a slightly modified version for two digit multiplication.

The Game


  • 4d6. Two dice are re-labelled 0, 1, 1, 2, 2, 3 (see notes below)
  • Graph paper (we are using paper that is roughly 20 cm x 28 cm, lines about 0.5 cm apart)
  • colored pencils
Taking a turn
Roll all four dice. Form two 2-digit numbers using the standard dice as ones digits. Then, use your color to outline and shade a rectangle in the grid so that:
  1. the side lengths are the 2-digit numbers you formed with the dice
  2. At least one unit of the rectangle's border is on the border of your block blob
  3. Note: the first player on their first turn must have a corner of their rectangle on the vertex at the center of the grid. The second player has a free play on their first turn.
  4. Write down the area of your rectangle
Ending the game
The game ends when one player can't place a rectangle of the required dimensions legally.
When that happens, add up the area of your block blob. Higher value wins.


"Counting" sides
The side lengths of the rectangles are long enough that counting on the graph paper will be irritating. Instead of counting directly, they can measure the side lengths. For our graph paper, the link between the measurement and the count is nice, since the paper is very nearly 5mm ruled, so they just double the measure. I think this is a really nice measurement and doubling practice, too.

Dice labels
Other labels could be used on the special dice. We chose this arrangement because of the size of the graph paper. Rectangles with sides longer than 40 often won't fit and we think we will even need some single digit rectangles to allow a fun game length. An alternative we are considering is 0, 0, 1, 1, 2, 2.

As an alternative to labeling the dice with new numbers, you could label them with colored dots and give out a mapping table. For example:
blue corresponds to 3
red corresponds to 2
green corresponds to 2
yellow corresponds to 1
black corresponds to 1
white corresponds to 0
This would keep the tens digit dice distinct from the ones digit dice and allow rapid modification if you want to change the allowed tens digits (just tell everyone a new mapping). Alternatively, you could create a mapping using "raw" dice and even allow more strategic flexibility from the players. I have a feeling that this would be confusing to most kids, though.

Reinforcing the distributive law
To facilitate calculating the area and reinforce the distributive law, you might have the students split their rectangles into two (or four or more) pieces and calculate the partial products. You can further decide whether to ask them to split the sides in particular ways or encourage them to find the easiest way to split to help them calculate.

Monday, August 1, 2016

Our math curriculum

Sasha Fradkin (who writes one of our favorite blogs) asked a question about the curriculum we use. My reply was getting long, so I decided to make it into a separate post.

Do we use an existing curriculum or are we making our own?

We are doing a mix. My wife prefers to have a linear curriculum as a guide and fall-back, in case there wasn't time to plan anything more customized. She currently uses:

  • RightStart/Abacus Math: ok, but not exceptional curriculum, highlight is the extensive use of physical manipulatives.  
  • Beast Academy workbooks: wrote more extensively about this in a review before. I think these create good jumping-off points for really fun conversations. 
  • DreamBox: for consolidation of standard skills, our enthusiasm for this is waning, rather than waxing right now (noted in same review as BA). 
We also use the CCSS math standards as a reference. I periodically check against the standards to see whether we are missing anything. If so, I will go to the Georgia Standards of Excellence, read through their activities for the related unit, and pick a couple that seem fun.

If I were forced to use only a single source, GSE would be my recommendation.
About Georgia Standards of Excellence
As far as K-5 math, this is a really awesome resource with a ton of great activities. For some reason, we find the webpage organization a bit confusing, so here is our quick recipe.  
To get to the great activities, I click the expansion menu in the right-hand box for the grade level of interest, then look at the curriculum map for that grade. I find the topic of interest, then click the link for the unit that covers that topic. The unit doc includes a lot of teacher background, which I mostly skip and focus on the activity descriptions.
Games and explorations
My personal preference is much less structured. I really like games and explorations and spend a lot of time exploring math activities on the MTBoS. Most of what I do with the kids is inspired by something I saw while doing my own play.

That said, there are some sources that are so good, we are essentially going through all of their activities:

  1. Mathpickle. Cannot say enough positive about this.
  2. Peter Liljedah's numeracy activities. Now that I notice them, I bet his good problems, card tricks, and resources pages will all have gems as well. 
  3. NRICH and Wild Maths.