Multiple Meaning Math

For my 1st grade students, all English language learners, I've been focusing on how the meaning of known words can be applied in math.  Concepts taught at this grade include addition, subtraction, counting coins, tally marks, telling time to the half-hour, and the attributes of shapes.  Since they also must be able to count by 2's, 5's, 10's up to 100, the number line and number grid because valuable tools to visualize the problems we work with in a more concrete way.

Still, the way we talk about math can be confusing!  For example, if you ask a 6-year-old to "count up from 2 to 5," processing the meaning is a challenge.  "Up," "to," and "from" have multiple meanings, and none of them will have been heard or seen by ELLs before when talking about a number line.  "Up" is above me, "to" is where I'm going (e.g. "to school") or what I'm going to do ("to eat lunch"), but rarely where I stop.  Finally, "from" usually indicates the person who gave me a gift, not where I started from.  So activities with a number line on the floor, with explicit instruction that defines the "math-meaning" of these words is helpful for all students.  

Another example of multiple-meaning words challenging understanding are the words "more" and "less" when applied to numbers, not visual/tangible quantities.  Consider: what would a child think when you ask "Which is more?" and the choices were two numerals.  I would imagine the thought processes might go like this:

"Hmm...the numbers are the same size.  They are close to each other.  Let me get my unifix cubes...wait, what was the question?"

So for the past two months, I've been teaching small groups during math stations, about the questions we often discuss that contain the words "more" and "less" and how we can consider those questions using manipulatives to explain our thinking.

Here is the vocabulary card I created to explain the meaning of "more" and "less" in math:

We started by identifying, between two quantities, which was more and which was less.  Then I extended the challenge into math questions using the comparatives "more than" and "less than" with kinesthetic learning.  We said together "more" while moving our hands apart, as though around a balloon being inflated; and "less" with our hands starting apart and coming closer together.  We also had a discussion about connecting the words "more" and "bigger," "less" and smaller. 

In another lesson, we read this math text:

Reading this book, which focuses on seeing "[quantity] more" animals, helped students connect more with addition.  They showed me how they could use their fingers or unifix cubes to find the answer.  They practiced writing the number models on their whiteboards (i.e. if we saw two more tigers, how many did we see?  3+2=5) and justifying why they chose to add, "...because more means bigger").  We also practiced extending this understanding to the number line.  I modeled, then they tried counting up or down (words I didn't use in these lessons; not yet) when we talk about more and less.  They started to show me which direction (left or right) they would count on a number line if we heard the words "more" or "less," and could explain why.

After 3-4 lessons about the use of "more" and "less" in math, I chose to give a formative assessment to see which students needed support with answering questions containing this words and how.  To do so, I included questions related to visuals, number lines, and simply words.  I gave my students the choice to use their fingers, unifix cubes, and/or the number line to explain their answers.  

In the following video, I talked with my student, who goes by AB, about the challenge question.  It was important for me to see that he understands "more" and "less" better when he approaches a problem with the number line; using unifix cubes to show "more than" is still a strategy that I'll continue to address.  Check it out and let me know what you think!