To get the students thinking and excited about today’s lesson! I write the digits 0 through 6 on 6 x 9 index cards. Then I write a comma on two index cards. I give one card to 9 students. I ask them to stand in a line across the front of the classroom. I call out instructions such as, “move the 6 to the hundreds place, move the 4 to the hundred thousand place, move the 1 to the millions place, etc. Have the rest of the class write the numbers in word, standard, and expanded form. Although, students are busy moving numbers, it allows me to check their understanding of place value.
MP2-Reason abstractly and quantitatively.
In this lesson I want my students to be able to explore different ways numbers can be written, and gain a deeper understanding of place value. These concepts are a vital piece of understanding estimation. I continue this method until students can work fluently with numbers. Most of my students are explaining their ideas mathematically!
After that, I briefly go over some basic rounding skills to build some background knowledge. I am careful not to probe to much, but give students just enough to support their learning. For instance, as I explain and draw representation I ask students the following questions:
Do you agree? Why or why not?
Does anyone have the same answer but a different way to explain it?
Do you understand what __________is saying?
Can you think of another way?
Some students are able to explain estimation from a rounding standpoint, I quickly explain that this is another way to estimate. However, I point out that using estimation allows them to check for reasonableness of their given answer.
MP1-Make sense of problems & persevering in solving them.
In this portion of the lesson students will work on their rounding skills using a number line. Since place value is a skill my students have mastered, I want them to really focus on using it to assist them in estimation(rounding). Hopefully, while working with numbers lines students will see that they are choosing the number closet to the number they are rounding.
I ask students to move with their assigned partner. How many of you like to save money? Of course everyone raises their hand! Well, who can think of a way that estimation can help you save.
Can someone explain how? (You can estimate how much something is before you buy it.) Yes!
During this activity I want you to estimate first, and then solve your problem. It is my goal for students to gain understanding of using estimation to check their problems for common errors made with paper and pencils.
I post the following question on the board:
Pam wants to buy 5 lolly pops that cost $1.95 each. When she buys them the cost is $12.25. Is that right? Explain? (If one lolly pop is $1.95 each is about 5 times 2 = 10, or 1.95+1.95+1.95+1.95+1.95= 9.75. So, $12.25 seems too much!
MP7-Look for and make use of structure.
What is the number closer to? It is closer to 10
How do you know? First I rounded 1.95 to 2.00. Since, Pam bought 5...so 5 times 2 is about $10.00.
Can you show me a model using a number line?
Some students used what they knew about number lines to determine what the number was closet to. I ask, why is rounding important. Rounding is important because it allows us to check the reasonableness of our answers. Great! I point out that rounding numbers should result in using number sense and not just following a rule.
When the time is up, students can share out what they have noticed. As students are busy sharing out what they have learned I use a rubric to gauge their understanding, or to see if any additional modeling is needed.
In this portion of the lesson I want my students to gain a deep understanding of place value and number sense. Additionally, I want them to become more fluent in explaining their answers. To start, I want to model how students should explain and reason. To do this, I post the question of the day!
MP2-Reason abstractly and quantitatively.
Carol wants to collect 400 stamps. On the first week, Carol collected 4 packs with 12 stamps in each pack. Daryl gives Carol 2 packs with 10 stamps in each of the packs. About how many stamps does Carol still need to reach 400 stamps?
Quick Check of understanding.
What does the problem tells us?
Carol wants to collect 400 stamps.
How many stamps does Carol collect?
She collects 4packs with 12 stamps in each pack.
How many does Daryl give Carol?
Daryl gives Carol 2 packs with 10 stamps in each pack.
Ok! Let’s look at what we need to know!
About how many stamps does Carol still need to reach 400 stamps?
For struggling students: In the modeling piece, I often refer back to base-tens and place value to help students gain a deeper concept of checking for reasonableness of their answers.
First, I am going to multiply 4 times 12 which equal 48. This is the total that Carol already had. What do you think we need to do next? Calculate the amount that Daryl gave Carol. Multiply 2 times 10 which is 20. I noticed that there are two totals. What do we do now? (Add them) I know 48 plus 20 is about 70. Since Carol needs 400 I think it would be easier to count by hundreds, but Carol only has 70. How much does Carol need to make 100. 70 + ___= 100. She needs 30 more. Right! Again, how much does Carol need in all. 400. Now that Carol has 100 how much does she need? 100 + ___= 400. Carol needs 3 hundreds more. Ok! Let’s think back for a moment. We added 30 plus 70 to make it an even hundred, however, 30 was added on to round 70 up to 100. So Carol still needs 330 stamps.
Depending on how well students respond I will repeat this model using a different word problem.
In this portion of the lesson I ask students to move into their assigned groups to work together.
Materials: chart paper, markers, highlighters, base-ten material
As students are working I will circle the room to check for understanding.
Each group is given Group Word Problems.docx to interpret, breakdown, and solve.
First, I ask students to write the word problem on the chart paper.
Next, I ask students to take about five minutes or so to read through it, and determine what the problem is asking.
Then, I ask students to box in the question portion of the word problem. This will help keep them focused on what they need to do. ( what does the problem tell us?) (What do you notice?)
After that, I ask students to underline key words, circle the numbers, and cross out any words that are not needed to solve the problem. Knocking out extra words and circling the working numbers assist students as they problem solve.
Now that students have simplified their problem, I want them to work a bit with the numbers they circled. To do this, I place some base-ten materials in each of the groups, and I ask them to represent the numbers using base-tens. After making their representations, some students ask if they can draw them on their chart paper.
Questions will depend on the numbers used in solving the problems :
What number is in the tens, hundreds, and ones place?
How many tens, hundreds, and ones do you have?
Can you write both numbers in written form?
What is 10 more than the number?
What is 10 less than the number?
How many more hundreds will you need?
After students have had time working with the numbers, I asked them to revisit the question they boxed in. What do you think we need to do to solve the problem. How much do you have so far? How much more do you need? Let's start by looking at what we have so far! It appears to be close to a hundred. ( multiples of tens are easy for students to estimate.) How much more do you need to make a hundred? Since you have a hundred here, how many more hundreds will you need to get the total amount? Now think back! you added on to the first number to make it a hundred. Was that one of the number you circled? No! What do you think we need to do to find the amount needed to solve the problem?
We continue with questioning until students are able to explain on their own.
In this portion of the lesson group volunteers will share what they learned! I will continue to take notes and use them to check or understanding. After students have shared out, I ask them to take about five minutes or so to write in their math journal about today's lesson. I remind them to be sure to explain using vivid details! Allowing students to journal about their lesson is more or less a running record to keep up with their growth in explaining their problems.