adding sums to 100
First-grade students are responsible for adding with sums to 100 as a means of understanding and applying place value concepts.
Addition to 100 focuses on adding 2 digit numbers to 1 digit numbers in cases where a new ten is and is not created. Strategies to add can include something as simple as using a known strategy like counting on and extending this strategy to these larger numbers.
When introducing strategies based on place value first work with cases that do not make a new 10 using both concrete and then representative models. Once students are comfortable with these models move to cases where a new 10 is created; again, using concrete and then representative models. And, all along the way, you will link these strategies to written methods as well.
The 5 examples listed are certainly not an exhaustive list of tools and lessons that could be used to teach this skill.
They are rather a sample progression from hands-on to abstract thinking!
Which step represents your students’ current level of understanding?
It’s easy for students to be initially overwhelmed when adding numbers larger than they have worked with previously. Linking known strategies to these new large numbers can help your students to find success and to begin to make connections to other strategies they can use.
Consider by starting with a strategy such as counting on. Try this: Tell your students a story about catching tadpoles. You had 42 in a bucket and then caught 3 more. How many tadpoles do you now have altogether? Show your students a picture of a bucket labeled with a 42 and a picture of 3 more tadpoles. How could they count to find the total?
Before introducing your students to addition of numbers to 100 there are prerequisite understandings that need to be in place:
- Addition puts parts together.
- Two digit numbers consist of tens and ones.
- You can represent two numbers and combine them to find a total.
When first introducing the concept of addition to 100 you are NOT going anywhere near the standard algorithm. Instead, you are aiming to provide your students experiences that will help them to build on these understandings. New understandings include:
- Tens need to be combined with tens, ones need to be combined with ones –they don’t mix and match!
- If 10 ones are put together, it will create a new 10.
Start simple with experiences that do not create a new ten in order to build this first understanding.
Try this: Provide your students with a simple story problem, for example “Sheldon went to the store and bought a new video game for $42 and also a bag of popcorn for $4. How much did Sheldon spend in all?” Talk about who was in the story, what they were doing and what you might need to do to find the total. Then provide your students with hands-on materials such as linking cubes, base ten blocks, play money or straws and rubber bands and allow them to model and explore as they find their solution.
Ask your students questions about how they might count to find the total and model counting all together.
Support your students in moving from hands-on tools to representational models such as place value drawings by creating explicit links.
Provide your students with a simple put-together type story problem and ask them to use hands-on tools to solve. Next, ask your students to share their method for putting the two numbers together. As they describe their hands-on model, draw a place value model to match. Be explicit when talking about how your place value drawing shows the same information as their physical model.
Next, ask your students to solve another problem. This time they are responsible for using concrete materials to represent and solve but also for drawing a place value drawing to match. Again, be explicit! If they show 53 using base ten blocks, ask where they showed 53 in their place value drawing. If they tell you that the total has 8 ones ask where the 8 ones came from in their concrete model AND in their place value drawing.
Introduce addition with regrouping in exactly the same way you did addition with no new ten.
The only difference here is that once your students put the ones together they will find that they have enough to create a new ten!
Base ten blocks are an ideal tool as they are a groupable model- your students can physically put ten cubes together to create a ten.
As your students are working and modeling, expect and require the use of math language! Ask your students what happened when they put their ones together. How did they create a new ten? Where did that ten come from? Were there any ones left unused? Where can we see those ones in the final total?
Adding sums to 100 is NOT about using an algorithm at this point. At this point your students are learning how to add sums to 100 but, more importantly, exploring place value by putting numbers together.
Just as you linked the concrete to representational drawings and models when there was no need to create a new ten, the same method is used here.
Provide your students with a simple put together word problem Sam baked 45 cookies last night and another 9 cookies today. How many cookies does Sam have altogether?
Ask your students to solve first by using a hands-on tool and then ask your students to draw a place value drawing that matches their model.
Will the drawing get messy as they show the creation of a new ten? It might! That’s okay! Your students are exploring place value and what happens when ten or more ones are put together. The focus is not on using an algorithm to find a quick and clean solution- the focus is on deep understanding of place value concepts!