Full Capacity!

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4.NBT.B.4 SWBAT to fluently add and subtract numbers using standard algorithms.

Big Idea

Working to their full capacity students analyzed word problems to practice on standard algorithms in order to become fluent in adding and subtracting numbers.


20 minutes

Materials: Dry erase boards, play money, markers

Skills: reasoning, subtraction, addition, explaining and making sense of 

To connect students in an unusual way, I ask them how many songs do they think can fit on one disk. Students sounded off with different numbers most of them were rather large.  You are all right!  A disk can be used to its full capacity.  Well today guys we are going to use our thinking skills to its full capacity to become more fluent in adding and subtracting by reviewing the use of standard algorithms.

MP1-Make Sense of Problems & persevering in solving them.

Now that students have worked with numbers and understand how they can change depending on the value of the digit, I want them to work with understanding standard algorithm. It is my goal to have them make sense of problems in order to help them become better problem solvers. Because I want them to work with numbers, I do not want to work them through by modeling. However, with careful questioning I will assist as needed.

To start, I invite students to have a seat on the carpet. I pose this question:

Tiffany wants to  purchased a new boat for $ 238.00.  She has $ 875.00.  Tiffany took out some paper and begin to rearrange 238 dollars as 200 + 30 + 6.  Why does she do this?  I ask students to explain their answers using play money if necessary.   I may ask how many ones, tens, and hundreds does she have. Some student may notice during the decomposition method of subtraction, there are sufficient hundreds and tens to solve the problem, but there are insufficient ones.  To solve this problem I ask students to solve their problems on their dry erase boards. I want to see if they can explain borrowing.

Some students give explanations, however, they are not using the mathematical terms. I will take note to model this throughout the lesson, and allow students additional time to explore explaining mathematically.

I work through a couple of more problems with to make sure they are grappling the concept here!

Group Work!

15 minutes

Materials: paper, pencils, base-tens material, play money

Skills: expanded form, subtraction, explaining and reasoning.

 In this portion of the lesson I ask students to move into their assigned groups to work on solving problems together.  Each group will have about fifteen minutes or so to answer and explain the following question about the word problem. To add  motivation to the mix, I yell loudly are you ready to use full capacity? They screamed yes we are!

Word Problem:

To solve 333 - 241, Pam wrote 333 as 300 + 30 + 3 =.  Why did she do this? MP3-Construct viable arguments & critiquing the reasoning of others. (e.g.. She used expanded form to group her numbers. Why? So that she could make sure she was adding the correct numbers.) 

 To further assist students who seem to struggle, I ask them to use base-ten material /play money. This will help them determine the distance between each number according to its place value.  I ask them to write their responses down on chart paper. MP4-Model with mathematics. Hopefully the modeling will help them translate the solution to the problem itself.


When you write the numbers in expanded form, what do you discover? The value of the digit.

What happens when one number has more or less tens than the other? In some cases it can make the number larger, or smaller.

 Why do you think Pam rearranged the numbers before subtracting?  Maybe she did not know how to align her numbers.

As students are working I circle the room to reinforce place value, and the steps to borrowing. When students time is up, I ask student volunteers to share out what they noticed. By sharing out, I hope students will enhance their mathematical understanding.


 students working.jpg

Show what you know!

15 minutes

Materials:  response sheet, pencils

Skills: subtraction, expanded form, problem-solving,  and reasoning skills

 Some of my students have explored many ways of adding and subtracting whole numbers. However, the standard algorithm starts with adding the ones and regrouping as necessary.  Because some of my students are use to solving math in one general way, I want them to use that because it makes sense to them.  To get them to see different ways to add and subtract numbers, I will allow them work on a mixture of problems requiring and not requiring regrouping.  To support my struggling students I will open up the opportunity to use number lines when adding and subtracting until they are comfortable visualizing it on their own.

 I turn students lose to show what they know! As students are working on their given task. I circle the room, to reinforce place value,  expanded form, and borrowing skills. For instance, I ask students why and how questions to see what they know. I will use students response sheets to determine the level of understanding, or to see if additional strategies should be set in place.

 Student Sample