Using children’s literature to enhance the understanding of place value and base ten in your math lessons.
I recently co-presented at a math workshop for teachers. In the workshop, teachers were to create a lesson that centered around the ideas of place value. It really amazed me that so many teachers had such misconceptions about our base ten numeric system. A deep understanding of place value is greatly tied to almost all that is done in mathematics so it is critical to have a good understanding of place value. So how can we make place value easier for kids (and adults) to understand? One way is to use children’s literature.
A Place for Zero
Poor zero. He wants so badly to be able to play Addemup with the other digits but he does not see how his number of zero fits in. After all, he thinks, zero is nothing. So he tries to work with Count Infinity to see if he can find his place. Eventually he sets out on a journey to visit King Multiplus and Queen Addeline. He was curious about multiplication and if that might help him to find his place.
One of the things that I like about A Place for Zero by Angeline Sparagna LoPresti is the vocabulary. Not only does it talk about numbers as digits but it also mentions infinity, factors, products, and binomials.
Millions and Millions
Picturing a million of anything is really difficult for children. There are two fantastic books that help children bring this number to reality. The first is A Million Dots by Andrew Clements. In this story, the author starts out with one dot and continues to add dots as he goes along. All the way through, he chooses a number of dots on that page and then provides real life illustrations of what that number would look like. For example at dot number 24,901 he states that this is the distance around the Earth at the equator.
The second story is How Much is a Million by David Schwartz. Similar to A Million Dots, Schwartz gives real life examples of what each number would look like. The difference is that he continues on to talk about a billion. A billion goldfish would need a fish bowl as big as a stadium to hold all of them. Developing a sense of large numbers is the focus in this particular story.
Sir Cumference and All the King’s Tens
Understanding how numbers move in value from one place to the other is foundational for all other mathematical operations. Sir Cumference and All the King’s Tens helps students to visualize the value of each digit in the place value chart. Visitors to the Royal Palace are grouped by tens and then by hundreds and ultimately by thousands. The illustrations and storyline help students to create a picture of how grouping numbers by ten easily lends itself to counting large numbers and combining them in other mathematical operations.
Two of Everything
Two of Everything by Lily Toy Hong is a Chinese folktale. When a pot appears in the garden the Haktaks, they are curious about how they will use it. They soon discover that anything that is placed in the pot is doubled. Of course there is a little bit of trouble that ensues but all is resolved in the end. It is a fantastic way to help students begin thinking about how numbers double.
One Grain of Rice
In One Grain of Rice, the Raja demanded that all the people in the village give him most of their rice harvest each year. He claimed that he would store it so that in a time of need, they would be able to use the stored rice. When the famine hit, the Raja refused to open the storage of rice and share it with the people. After performing a good deed that was acknowledged by the king, the girl, Rani, devised a plan to get rice to the people of the village. As her reward, she asked the Raja for just one grain of rice that day, but that he would then double the amount from the previous day for the next 30 days. The Raja thought this was a silly request because what would she do with just one grain of rice. He soon learned the power of exponential numbers just as your students will after reading this story.
Using the Books
There are many ways that you can use these books to help students to clarify their thinking around place value. Depending on the age of children that you are working with and the standards that you are working on will determine which books are the best for your lesson or unit.
Here are some very general ways that you can use these stories to enhance your instruction.
Read One Grain of Rice as a springboard to exploring exponents. Read only up to the part where the Emperor gives the doubled rice on the fourth day (8 grains) and record the pattern that is being created. Have students make a prediction about how many grains of rice there will be at the end of 30 days. Then allow students to work in groups to find the answer.
Use one of the million books to help students visualize large numbers. Then have students bring in 100 of some sort of snack food (raisins, cheerios, pretzels, etc.) and then combine them in a bowl. As you eat the snack, talk about how many students brought in 100 treats and how many there are all together in the bowl. Although this will not create a million, it will help students to concretely see larger numbers.
A Place for Zero can be used for a small group of students who are having difficulty understanding how zero fits into our number system. It can also be used as an introduction to a unit on number sense. Present students with two numbers, 27 and 207. Simply ask them if they are the same number, why or why not? This will prompt a discussion about how zero is not nothing but has a very valuable place in our number system. After all, would you rather have $27 or $207?
When you are teaching addition of the same number or introducing mulitiplication, Two of Everything is a great way to have students begin to combine numbers to see how many they will have in the end. You can have students draw number models, use counters, or draw pictures of things like 2 apples and another 2 apples is how many? Use larger numbers for older students.
Base ten blocks are a great addition to the story Sir Cumference and All the King’s Tens. After reading the story, you can have students simply build numbers using base ten blocks. More advanced students can build arrays to show various muliplication facts and students could even look at a number a determine how many tens are in the number. For example 34,456 has 3445 (3445.6 for more advanced students) tens in it. How many tens are in the hundreds place in that number? 45 (or 45.6). How many tens are in the thousands place? 445 (or 445.6)
These activities are just a small sample of ideas about how to use these books when teaching place value. You are sure to come up with some fantastic ideas of your own. Just remember that literature is important in math and bringing it into your math lessons will help students understand difficult concepts a little easier.
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