- Take it slowly
- Use multiple representations
- Ask the right questions
Let’s take a look at each idea individually.
Take it slowly
“However, if place value concepts are to be meaningful, children need to know more than what digit is in the tens place and what digit is in the ones place. They need to know that the underlying structure of two-digit numbers is based on organizing numbers into groups of tens and ones. This understanding is critical and basic to successful future work with larger numbers and decimals.”
It is a major milestone for a child to transition from counting items one-by-one to understanding that we can count a group of ten as a single unit. This skill is call unitizing. Students should have ample experience working with numbers from 10 to 20 and seeing that numbers can be thought of as ten and some more before going on to greater 2-digit numbers. If a student can’t tell you immediately that a ten and 3 ones is 13, they probably need more practice with numbers less than twenty.
Use multiple representations
Another great way to count the days in school is to use ten-frames. I found this picture on Pinterest a while back, and I love it!
Van de Walle tells us that traditional base-10 blocks are far too abstract for students at the beginning of their place value journey. Why? Because students can’t physically combine ones to make the ten and they can’t break it back into ones. Instead, students should use groupable materials, such as linking cubes, bundled straws, beans in small cups, etc., so they can build a ten and then break it back into ones.
Another great tool for exploring place value is the hundred chart. Because the structure of the chart groups numbers into rows of tens, it is a useful representation for exploring concepts such as ten more and ten less.As students are representing 2- and 3-digit numbers with concrete materials, be sure to connect their hands-on learning to the abstract symbols behind the models they are building. This handy little holder and set of place value cards helps students see the values behind (literally…ha ha) the digits. I made it to show numbers through the hundreds, but of course you would start with only tens and ones.
Let’s go back to how you might use this with the straw mess from the 76th day of school. As students count out bundles of tens, use the cards with the multiples of tens to keep count of how many straws they have. So when they count 10 straws and bundle them, put out the card that says 10. Don’t put it in the holder yet–just use the cards to keep track. As they bundle another ten, replace the 10 card with the 20 card. Keep doing this until they are showing the 70 card to represent the 70 straws that are now bundled. They count the final 6 straws and take out the 6 card. Now put the 70 card and the 6 card in the holder so they can see how the 70 bundled straws are shown as 7 tens.
Of course there are lots of other uses for the cards. You can grab your own set of cards and holder for free by clicking here!
Ask the right questions
- what does that mean?
- can you show me that with … (linking cubes, base-10 blocks, etc.)?
- can you draw that for me?
- how is that different from having the same digit in the ones place?
Head on over to the next stop along the hop and see what The Recovering Traditionalist has to say about place value!