Ordering Numbers

I'm trying to stay caught up on blog posts, but there's so just so much that happens in the first few weeks of school!

I took these pictures two weeks ago while we were working on ordering numbers.  Here the kiddos are working to build towers of numbers and put them in order, least to greatest.  As I started to write about this activity, I realized that we've already moved so far beyond this lesson.  Today we began finding different combinations of numbers that can equal 7 (i.e. 5+2, 4+3, 6+1, etc.).

Nevertheless, I'm reminded of how essential it was that the kiddos started with these foundational activities.  We begin our year with a series of "games" where the kiddos match numerals to quantities, order quantities, determine less and greater, and count specific quantities.  Although we progressed through these lessons quickly, they really set the tone for the year: we developed common math language, identified strategies for counting and double-checking, and established the importance of counting and comparing accurately.

These first few weeks have also been a valuable time for me to gather anecdotal notes.  As the kiddos worked, I walked around taking notes about how they read numbers (do they know the difference between 6 and 9?), how they count quantities (do they start at 1 each time or can they group small amounts and count on?), and how they order and combine (do they have to count up or do they have an instinct about larger numbers?).  I have also been able to pull small groups of students who need to shore up their basic skills (I had a few kiddos who were not able to accurately draw or count a group of 20 objects.)

More to come on the math games that were introduced during this unit...

Strategies for Counting

This summer I was fortunate to attend the 5-day workshop Investigations in the Classroom workshop, hosted by my school. The training focused on how children develop number sense and mathematical reasoning skills.  We were able to explore some of the games and activities that are part of the Investigations curriculum and consider how we might adapt or extend these learning experiences to meet the needs our students.  

One of my biggest take-away from the sessions was the difference between strategies and tools.  As a math teacher, especially of young mathematicians, my hope is that my kiddos develop many strategies for solving math problems. I want them to be able to approach a problem in different ways so that, eventually, they can find the most efficient and practical way to solve it. 

However, too often, we end up teaching students to use the same strategy with a variety of tools.  For instance, students may learn to add using their fingers, cubes or counters, and by drawing pictures, but they may only use the simplistic strategy of "counting all" (starting at 1 and counting up).  Similarly, students can learn the "counting on" strategy (starting at the larger number and counting up) using their fingers, a number line, and a 100-chart.  

While tools, such as the 100-chart, are necessary and valuable for young learners; it is important to emphasize the strategies that students choose, rather than just the tool, so that the students can become critical of their choices.  I often see kiddos, especially when I'm tutoring struggling older students, who are reliant on tools, like pictures or number lines, and can not analyze a problem to choose a creative, logical, or more effective strategy to find a solution.

This year, I am trying to be very explicit with my kiddos about strategies.  I made a chart to remind us of the strategies we already know; as the year goes on, I'll add to it.  When a kiddo volunteers to share how he solved a math problem, I encourage him to name the strategy he used and then explain his tool (if any). We are currently playing a lot of games where the kiddos are combining numbers (more on these games later) so they are getting lots of practice explaining their strategies with partners as well.

The Power of 10

In first grade, I put a great deal of emphasis on learning combinations of numbers that equal ten.  When I started teaching, I didn't fully understand how important it was for young students to develop fluency with the number 10 and internalize these combinations.  It wasn't until I started tutoring 2nd graders who are behind in math, that I realized how critical it is for students to understand that not only does 5+5=10, but also 8+2 and 7+3 and 3+7.  Because we have a base ten number system, knowing these combinations is actually the foundation for understanding place value, estimation, addition, subtraction, and mental math with bigger numbers.  

Through our Investigations curriculum we have a lot of games that reinforce number combinations up to and equal to ten.  In addition to these games, I have started using transition time to review key facts.  The kiddos really enjoy when I toss a ball and call out a number between 0-10, then they gets to toss the ball back and say the number that will equal 10 (like 1 and 9 or 4 and 6).

I urge the kiddos to "put away their fingers and turn on their brains" to recall these combinations quickly.  I know that the faster and more automatically they can connect numbers to equal ten, the more comfortable they will be to add and subtract.  Once the kiddos have committed these combinations to memory, they are able to use the "get to 10" strategy for adding larger numbers.  For example, in order to quickly add 8+4, the kiddos can "get to 10" by taking 2 from the 4; then they know there are 2 left over so there are 12 all together.  Eventually, the kiddos can also use these primary combinations to add 2-digit numbers, such as 40+60.  If students know that 4+6=10, they know that 4 tens (40) plus 6 tens (60) equals 10 tens (100).

Although we practice these combinations throughout the week, we really work on building confidence and teaching mental math strategies on Fridays.  More to come on our "Fluency Friday"routines and Math Minutes!

Measuring and Counting

The week before Winter Break we took a little step back from addition and subtraction to do a short unit on measuring and counting strategies.  

This short Investigation started by having the kiddos trace each other's feet.  Of course, the kiddos loved this!  They worked carefully to trace around their partners' shoes and get an outline of each foot.  Then we talked about different ways to the we could measure our feet.  I briefly introduced words like perimeter, length, and width as the kiddos made suggestions for measuring around or across the outlines.  We eventually decided that we would estimate the area of our feet by filling the outlines of our feet with square inch-tiles and counting the tiles. 

As the kiddos arranged and counted their tiles, I walked around and took notes on their strategies.  I made suggestions to individuals and partners about how to improve their accuracy and double check their counting.  Some of the kiddos counted the tiles as they put them on the outline and again as they took them off.  Some of them slid each tile off the outline as they counted it, while others organized their tiles into stacks or piles and counted at the end. After everyone had a completed the task, the kiddos shared their strategies with the class. Then we recorded our total numbers on a chart.  

The chart started like this: 

Once we had our chart, I posed the question to the kiddos, "is this the easiest way to organize our data?"  Our next unit is going to focus heavily on graphing, so I wanted to the kiddos used to the idea of different ways to organize information.  The little guys suggested that perhaps we could group the like numbers together.  I pushed them further to think about how we could write the numbers to quickly tell what size was the most and least common and which numbers were the biggest and smallest.  Eventually, our chart looked like this:

The next day, we tried different materials to measure the area of our feet, such as pennies.  This was a great anecdotal assessment of how high the kiddos can count, since most of their outlines held 40+ pennies.  After break we will be working on counting, writing, and reading numbers over 100!