I am not sure when I learned how to write numbers in expanded notation, but I am certain it was not in 3rd grade. Students now are expected to learn how to write numbers in expanded notation as early as 3rd grade here in Texas and I am sure that applies to other states as well. But why? It is part of a push to help students understand the relationships between places and digits in our base ten number system. It can seem difficult at times, but with hands on activities and a lot of practice, your students can master expanded notation.
One method I find to be very effective is using play money:
Give your students a number. Guide them to use their play value money to model the number.
Then ask them “Ask “How many hundred thousands?” Tell “Expanded notation shows the number in each place times the value of the place, so 3 hundred thousands is 3 x 100,000.”
Continue questioning and guiding students to use play money to help them write the numbers.
You can download my play money for FREE by clicking the picture above.
For more great place value ideas, check out my Place Value Board on Pinterest!
I like place value blocks. They are a great concrete model for helping students to understand the relationship between ones, tens, hundreds and thousands. Students can count the blocks and set them side by side to see that ten ones is the same as one hundred or that one hundred tens is equal to one thousand. I also think it is important to use other examples for students to find meaning in the base ten system. In early grades we see students bundling straws and or popsicle sticks to learn grouping in tens and hundreds. A lot of teachers have students bring in objects to count on the hundredth day of school and sort them into groups of ten to see the relationship between ones, tens, and hundreds. These are terrific! But … what about older students? What about the relationships in the thousands, millions, billions?
For years I used blocks to teach and review base ten from ones through one thousands and then showed the students the patterns on the place value chart. One year I borrowed thousands cubes from other teachers to show my students a concrete example of ten thousand. (It was tall). This is a great concrete example for a lot of the students, and I still use the blocks (see my blocks post here). But not for all. So, what other models can we use with older students?
Money! Yup! Students seem to like talking about and playing with money! So I started using that play money from my manipulatives kit to help students see that the relationship between place values isn’t always about size, sometimes it is about WORTH (value)! So I took the fives out and we would use the play money to practice trading 10 ones for a ten, 10 tens for a hundred. And then I showed how that pattern repeats on the place value chart. Works great! But … most sets of play money don’t have the bigger bills … so … I made my own play money!
Now I have bills from the ones to the millions! I had a student ask me last week when we were working on this if there was really such a thing as a ten thousand dollar bill. I told her I wasn’t sure, but maybe we could research money to see what kind of bills the US Mint makes! Maybe I will have time to do that tomorrow! 😊
It is that time of year again! Time for jelly beans, eggs, bunnies and baskets! There are so many ways to use Easter excitement to keep your students engaged in classroom lessons. Here are some of my favorites from around the web:
One of my favorite activities this time of year is a Math Egg Hunt! Buy a bunch of plastic eggs and stick problems inside the eggs. Hide the eggs around the room. Give your students a record sheet or a piece of notebook paper and let them hunt and solve math problems. Print your own problems or get mine FREE here.
Task Cards Save Paper: Using task cards can cut down on the number of copies and paper used because you don’t need to make a set for each student and if laminated or kept in protective sleeves, they can be used for years without printing new copies.
Task Cards Increase Engagement: They add to student engagement because they add novelty. Paper and pencil practice is certainly useful, but can become dull and routine. Using dry erase markers on a task card can mix things up a bit. Also, task cards can be printed with fun colors and clip art to add interest for the students.
Centers and or Work Stations – Print cards and keep in small containers or baggies. Have students work in pairs or groups solving problems on task cards and recording on a record sheet. I like using record sheets for two reasons. One, the students are more likely to stay on task if they know they will have to turn something in at the end of the center. And, the other reason, I like to look over the record sheets to see if students need re-teaching or extra help with the skill/concept worked on in the center. If you do not have a lot of copy paper you can always have students use notebook paper to create a record sheet. Have them write the name of the center on the paper and then number or letter their answers.
Whole Class Cooperative Groups – My suggestions for whole class would be the same as for work stations & centers except you would need one set of task cards for each table group. After learning or reviewing a concept with whole class, the students could work on the cards with their table groups. After the group work you could have a class discussion about the task cards as a way to wrap up. Another whole class activity which would require only one set of task cards is a “Scoot” or circuit. To set up a Scoot you have a different task card on each desk and have the students work in pairs rotating around the set of task cards in numerical or alphabetical offer. Some teachers will set a timer for scoot and others will let students move as they finish. For a FREE “Scoot Record Sheet” that can be used with any set of task cards, click here.
Are your little leprechauns looking for a pot of gold? St. Patrick’s Day can be a lot of fun and also educational! Here are a few great ideas!
I absolutely love crafts for any occasion! Here are a few fun crafts for St. Patrick’s Day:
Leprechaun Mask by Abc Creative Learning
Paper Strip Shamrocks by Sugarbee Crafts
Water Bottle Shamrock Stamp by Crafty Morning
I guess it is no secret! I also love Math!
Lucky Charms Graph by How to Homeschool My Child
Ten Lucky Leprechauns by One Sharp Bunch
March Math Freebie by ME!
And just for fun …
St. Patrick’s Day Joke Cootie Catcher by Bren Did
Leprechaun Poop by Penny Pinchin Mom