Notice we kept as many tools in place as we possibly could. We were getting somewhere! After practicing this a bit more, I was able to bring in the idea of expanded form with number cards, and then even write the equation: Then we put our hands on the 50 (or what the 5 stands for): So I asked them to put their hand on the hundred, what the 1 stands for: So we did some practicing, I figured if they could make the number, they could identify parts of the number in what they made.
“What do you mean what does it stand for?” I asked, “What do you guys think that the number 5 stands for in this number?” In the photo below they made the number 158 with bundles of sticks (in 10s and singles), cubes (in stacks of 10 and singles), place value blocks, and ten frames. They STILL didn’t understand what the numbers stood for when the number was in standard form. I knew they could make these numbers with tools, show them with ten frames and write them with much practice…but get this. I STILL learned my lesson the hard way with assuming things of children. The representational part is a picture form of the tools/number, and the abstract part is the actual number itself.
The concrete part is the tools, the actual quantity of what we are using. So what I do now is use my favorite approach, the concrete-representational-abstract string of learning. Place value simply is a way of understanding quantity in parts or chunks. Expanded form isn’t hard to teach with the right tools, and it will greatly enhance students understanding of place value. Expanded form is a way to deeply understand place value, but because back then I was a young and desperate, I thought anything that was hard to teach was worthless. Now, 11 years later I am seeing the error of my ways. To the other teacher I said, “What is the point of teaching expanded form anyway? There is no point in learning this!”
#Expanded form how to
I was frustrated that my students weren’t understanding what expanded form (that 145 is 100+40+5) was, and had no idea how to teach it for them to understand it conceptually. It was because of my inexperience and my inability to understand math at a deep level during my second year of teaching. Of course, Exit Questions are asked and Passports are used at the end of activity to bridge from the activity content to the way a student will need to answer a high-stakes test question about the concept.OK, I’m going back in time to tell you something totally ridiculous that I actually said to another teacher. The winning pair turns over the next number and play continues as time allows. Answer Keys are given to the Leader and Co-Leader. Whichever pair does this first wins that round and receives 5 points.Įvery pair who has correctly created the expanded form of the number earns 2 points. The game, “Excellently Expanded,” is hands on, engaging, and deepens a student’s understanding of how to compose and decompose numbers up to 999,999 using expanded form.Įach pair of students arranges their expanded form cards so they may easily and quickly create the expanded form of numbers.Īfter the leader turns over a number card, pairs of students try to be the first ones to create the expanded form of the number and be able to say what they have created. How do you make expanded form hands on and engaging? …method of writing numbers as the sum of powers of ten or as the sum of its units, tens, hundreds, etc.įor example, 3000 + 400 + 10 + 7 is the expanded form for 3417.īut, if you’ve searched for this blog, then you’re really wanting is the answer to the next question. …a helpful way to rewrite numbers in order to show case the place value of each digit. …the sum of each digit multiplied by its place value. …the writing of a number to show the value of each digit.
What is expanded form and how do we make the practice of expanded form hands on and engaging? Posted Septemby Glenna Tabor & filed under Balanced Mathematics, Differentiated Instruction, Engaging All Learners, Guided Math Instruction, Manipulatives, Math, Math Activities, Math Games, Math Stations, Number Sense, Small Group Instruction, Small Groups, Tabor Rotation, The Tabor Rotation Framework.
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