My picture book Penguins on Parade uses a purely fanciful problem to illustrate students making sense of counting by tens from a number that doesn’t have zero in the ones place. The characters in the book enjoy imagining the penguin parade starting with 8 penguins followed by groups of 10 penguins. Their teacher Ms. Green asks them to figure out how they could count the penguins by tens starting at 8. Share this book with your class and show them characters deepening their understanding of tens and ones as they tackle an unfamiliar problem.
Trevor is frustrated by this problem since he’s never been told how to do it. But his partner Zoe perseveres and engages him in using Ten-Frame Cards with dots on them to help them figure out the subtotals for the count. Then they examine their list, 8, 18, 28, 38, with their classmates and begin to understand why adding on a ten increases the number in the tens place while the number in the ones place remains the same.
Two other classmates Ellie and Kayla use an open number line (or empty number line) to help them figure out what they get when they add tens onto 8. They break up each ten into a 2 and an 8 to make the fewest jumps they can to add on a ten. They know it is efficient to jump to the next multiple of ten and then add on the amount left in the ten. They are applying their knowledge of the number pairs that make ten and their understanding of counting up and down on a number line.
Explorations like this are much more powerful than just remembering which place is the ones place, which place is the tens place and adding ones to ones and tens to tens. Experiences like this help students understand that the 4 in 47 means 4 because it is 4 tens, but also means 40 because 4 tens are 40.
The characters in the book model how they are learning to use the Standards for Mathematical Practice. Your students will see this class sharing ideas and helping Trevor gain confidence in his ability to make sense of new problems!
