Recounting the First Half of the Year

These are a few math activities that have happened in January through April, taken from reporting to Self-Design distance learning program:



January

• SpiderGirl revisited addition, subtraction, and multiplication through playing "store." She sold and bought things for $1, $2, $3, or $1/2 each, selling 2 to 9 multiples of an item. The buyer would pay for the purchase with exact or inexact change, receiving money back if need be. We also used visual patterns in the counters to make counting easier. SpiderGirl is really getting the hang of making change, though if I tell her the change is a ridiculous amount, she still doesn't realize it until I ask her to stop to think about it. Counting out multiples of 2, 3, and 5, is coming more quickly with practice. She still shows a strong understanding of using one type of counter to represent 10 of a another type of counter.
• SpiderGirl was reaching out for some new math concepts to work concretely with. She settled on understanding integers. We worked with two different colours of counters, one to represent positive and the other to represent negative. With the counters, she demonstrated a solid understanding of a negative combining with a positive (of the same absolute value) to make zero. She also successfully added several combinations of positives with negatives. For example, 2 + -3 = -1 and 5 + -2 = -3.

February

• With Chinese New Year, SpiderGirl got quite a lot of spending money in all sorts of denominations. She spent the last couple of weeks taking out her change and counting it and playing with it. She has gotten really comfortable making dollars out of quarters and is on her way with dimes and nickels. She is also making up 25 cents using dimes and nickels in various combinations.
• This week, SpiderGirl has been playing a game called "Cups and Beans" with me, and a variation of it, "Bean War." The games use painted dried beans as counters (painted side for positive and unpainted side for negative). We toss the beans and count the total. The person with the greater number wins the round. We have also been relating the exercise to holes with missing dirt, and owing and having money. SpiderGirl is demonstrating a strong understanding of comparing integers (greater than and less than).
• SpiderGirl is really getting a good sense of how the days arrange themselves into weeks and months since working with her own calendar to keep track of events that are important to her. After indicating an interest in better understanding the year, we cut a piece of paper into 12 equal pieces, labeling the months on them. A long discussion ensued, where we talked about where birthdays in our family fell, what months belonged to which seasons, how we could divide the year into halves, thirds, quarters, sixths, and twelfths.

March

• SpiderGirl constructed some geometric objects using nets. Here are the cylinder and the octahedron. She also made a cube, which … got squished before it could be photographed. SpiderGirl observed that the octahedron is two pyramids stuck together and that the cylinder is made of a rectangle and two circles. She also observed that "octahedron" sounds like "octagon," and we talked about prefixes: ‘octa’ means ‘eight,’ so ‘octahedron’ means ‘eight faces.’ SpiderGirl counted the faces herself. This led to further discussion about other prefixes, such as tetra, penta, hexa, hepta, nona, and deca.

April

• One day, SpiderGirl was talking about patterns, and I introduced her to some patterns that didn’t repeat. She understood right away, and picked two of the patterns to continue. We went off on a tangent practicing writing the ‘2’ the way I write it (with the loop). Then, SpiderGirl made some patterns for me to extend. She made one that was repeating, but only gave one iteration, and we talked about needing enough information to see patterns. She made a pattern of growing triangles (bottom), and a 2-dimensional pattern that increased in size going right and decreased going downwards.