I post this table on the board or on an anchor chart:
Kind of bean |
Number of beans |
Pinto Bean |
513 |
Navy Bean |
123 |
Black Bean |
412 |
Red Beans |
220 |
I ask students: How many beans do I have in all?
I allow students to work on white boards to solve this problem using the strategy that they think is best. Students have hundreds, tens, and ones blocks available to them as well as cubes that are bundled into groups of ten. Some students might draw hundreds, tens, and ones. Others may add two of the addends at once and then add the sums. Others may attempt to add all four together using regrouping.
As students work, I circulate to determine which strategies students are using and what common misconceptions/ pitfalls students have.
NOTE: The sum of these four numbers is greater than 1000. This was a purposeful push for my students since we had just started discussing the thousands place in math meeting. However, if your students are not ready for the thousands place, simply change the numbers--the lesson will still work!
Turn and Talk: What strategy did you use to solve this problem?
I give students a minute to discuss their strategy with their neighbor. I listen for strategies to help me decide who I would like to share.
Now we are going to have a strategy share. I want you to share your strategy, why you chose it, how it works, and how you were able to get an accurate answer.
Some students may suggest adding the four numbers in a column, others might suggest adding two of the numbers at a time and then adding sums. Finally, some students may suggest decomposing the numbers into hundreds, tens and ones to add them.
I have two-three students who used DIFFERENT strategies share. As students share their strategies, write their strategies on an anchor chart entitled “Our Strategies for Adding Four Three-Digit Numbers."
To encourage student buy-in, I often "name" strategies after students and have them write their names on the anchor chart next to the strategy they shared.
As students share their strategies, I make sure that they are modeling/ explaining the strategy so that other students will know how to use this strategy. To guide student thinking, I ask questions like:
-Could you explain how you set up your problem using your strategy?
-How do you check your work?
-Why did you choose this strategy?
Now that we have worked together to find strategies for adding four different three-digit numbers. We are going to work in pairs to solve a similar problem during our guided practice. You can use any strategy that works for you and I will leave our strategy share chart up to remind you of some potential strategies.
I allow students to work in pairs (or independently) for 7-10 minutes. As students work, I circulate. I attempt to get to every pair to listen in, observe what strategies they are using, and prompt when necessary using the following guiding questions: (1) What strategy are you using? (2) How are you making sure your work is accurate? (3) Why did you choose that strategy? (4) Show me how you solved your problem...
If time permits, I have students come together and go over the problem, stopping to highlight the strategies used by different students. Check in with students who got the wrong answer or who chose a strategy that did not allow them to be accurate (i.e: drawing ones).
Independent practice is differentiated based on student understanding of this concept. These independent practice groups are fluid and I determine grouping based on understanding and fluency in the guided practice section as well as overall mathematical fluency (i.e: students who struggle with regrouping are placed in the intervention group).
During independent practice, I will spend most of the time working with group A (intervention) to solidify the strategies that they are working on.
All three groups will have access to math manipulatives (place value blocks or cubes bundled into groups of tens).
Group A: In need of intervention:
Students will add four 3-digit numbers and will not be required to regroup. This group will focus on breaking down the numbers into hundreds, tens, and ones using place value blocks or drawings. Using blocks or drawings they will then add the numbers together--this activity will give them a strong foundation for regrouping.
Group B: Right on track
Students will add four 3-digit numbers and will be required to regroup.
Group C: Extension.
Students will add groups of four and five 3-digit numbers and will be required to regroup.
When students have finished working on their independent work, I bring everyone back together. I have one student from each group share a strategy that worked well for them.
This process allows students to hear the strategies for a final time and allows students to share why certain strategies work well for them.