Slowing down with place value
Lesson 1 of 5
Objective: Students will be able to refine place value skills to multiply numbers by 10, divide by 10, name numbers to one million with base ten numerals.
As students enter the classroom, I am jamming out to this song. They are strongly encouraged to sing along with it. This helps solidify their math facts. We practice our fluency with the basic multiplication and division in many ways. This is just one way.
My students LOVE this video series. They really get into it and dance as well. I let them move and groove as long as they are being appropriate. They must count by threes and have me see them and hear them if they want to dance.
I love magic. I use magic all year long as a way to engage my students. Before I start doing magic tricks we have many discussions centered around the fact that I am really NOT magic and that these "tricks" really work mathematically. I love when my students figure out a how a trick works by analyzing number relationships (MP.1), looking for patterns (MP.7) and convincing their friends and parents that they know how the trick works (MP.3). I have math practice posters hanging in my room, and refer to them daily. I explicitly point out that when we look for patterns and analyze number relationships we are using MP.1 and MP.7. I also tell them how important it is to be able to communicate their math thinking, MP3. The following trick is the third number trick I will be showing students.
Ask a friend to write down a number (any number with more than 3 digits will do, but to save time and effort you might suggest a maximum of 8 digits).
Example: 83 972 105
Ask them to add the digits.
Example: 8+3+9+7+2+1+0+5 = 35
Ask them to subtract this number from the original one.
Example: 83 972 105 – 35 = 83 972 070
Ask them to select any digit from this new number and strike it out, without showing you.
Example: 83 97
Ask them to add the remaining digits and write down the answer they get.
Example: 8+3+9+7+0+7+0 = 34
Ask them to tell you the number they get (34) and you will tell them which number they struck out.
The way you do this is to subtract the number they give you from the next multiple of 9. The answer you get is the number they struck out.
Example: The next multiple of 9 here is 36 (9 x 4 =36)
36 – 34 = 2 and there you have your answer, easy isn’t it!
Note: If the number they give you after step 5 is a multiple of 9, there are two possible answers then you simply tell them that this time they crossed out either a 9 or a zero.
I will repeat this trick many times through out the year. I have one day a month that students only come for half of the day. On these days, I am able to spend time with my students and guide them in understanding how certain tricks work. Some take longer than others. This is one that would take quite a bit of time for students to wrestle with. I guide them with questions that allows them to start thinking about multiples and we then often do a trial and error. Once students figure out that 9's are unique and at the root for many magic tricks, they get very good at looking at patterns, gathering data, and trying different numbers.
Begin this lesson by having students complete the worksheet from the day before. This is an independent practice worksheet that students started in the previous lesson. It is important for students to work independently on this practice in order to build their conceptual knowledge of naming numbers to a million.
Upon completion, students will correct their own work using a red pen to show when they fixed. I have students fix their mistakes as we go when we correct and talk about work together. I think it is important for them to see how to fix it, and do so immediately, rather than students waiting for me to give them the worksheet back several days later when we have already moved on to other practice.
From observing students during the preceding days, I will use this independent practice as a formative assessment. I will group students based on the teaching schedule who need more practice or other ways of learning the material in order to be successful.
Below is what I really hoped and THOUGHT we would get to. We did not have time at all! I have been surprised at my students lack of number sense. As a result. I slowed the lesson pacing down. Today's worksheet was done mostly whole group. Students independently completed side 1, but struggled more with side 2. They are very reluctant to draw a place value chart... almost as if they think it's bad or wrong to use a pictorial or visual representation. I will be emphasizing this much more in the next few lessons.
Students will spend the rest of this class time practicing multiplying and dividing whole numbers by 10, adding commas to numbers in order to read and write correctly, and work on naming a number with tens, hundreds and thousands. Students will rotate with their partner through three stations.
Station 1- Correct Commas
Station 2 - Show what you know at the whiteboard
Station 3 - Number Name Match
I want students to use a place value chart because so many of my students think of place value as simply naming the place a digit is at. In fourth grade I want my students to understand the concept of ten times more than and ten times less than. I want them to see how the digits move to the left every time they multiply by 10, rather than simply adding a zero onto the end of their original number. The place value chart allows students to use pictures if needed as well. Students can draw 2 circles in the hundreds place to represent two hundred and then draw two more circles TEN times to see what is happening to those two hundreds when they multiply by 10.
Place value plays a critical role throughout the grades in the development of computation strategies. For example:
364 + 347
- Break the addends into hundreds, tens, and ones, then combine the parts: 300 + 300 = 600, 60 + 40 = 100, 4 + 7 = 11, 600 + 100 + 11 = 711
- Transform the problem into an equivalent problem that uses landmark numbers: 364 + 347 = 361 + 350 = (350 + 11 + 350) = 700 + 11 = 711
24 x 21
- Break one of the numbers into 10's and 1's and multiply the other number by each of these parts: 21 x 24 = (10 x 24) + (10 x 24) + (1 x 24) = 240 + 240 + 24 = 504
- Change one factor to a landmark number, then adjust: 24 x 21 = (25 x 21) - (1 x 21) 20 x 25 = 500, so 21 x 25 = 525, 525 - 21 = 504
All these strategies rely on knowledge of place value: understanding how numbers are composed of tens and multiples of tens, knowing the place of a number in the number sequence, knowing the relationships of numbers in the problem to landmark numbers, understanding how landmark numbers behave when they are added or multiplied.
Student debrief - Wrap Up
Since the independent practice was done mostly whole group, I choose not to do any exit ticket or homework for today's lesson. I still feel my students need more practice and the ability to gain confidence in their skills. One student that is struggling did have an "ah - ha" moment today which is always so gratifying as a teacher. She told me that her favorite thing she did today was math. While she is not yet where I want her to be in terms of place value knowledge, hearing those words and her willingness to grow and learn from her mistakes was worth all the frustrations the lesson had brought me earlier.
As a debrief, I modeled similar problems to the independent practice. I had one student share her solutions. She chose to use tallies in her place value chart rather than circles (dots) or numbers. She pointed out to all of us that it got very confusing to see when she bundled a ten. This kind of self awareness and reflection from students is very positive to see and hear. I modeled using the place value chart as an effective tool for conceptualizing what is happening when you have 20 hundreds and add 11 more hundreds to it and similar problems.