Today's Number Talk
For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I am encouraging students to represent their thinking using an array model.
Task 1: 6 x 5
For the first task, I asked students for the solution. They said, "30!" Then I said: Okay, great! Now show me how 6x5=30! Sometimes we focus so much on getting the correct answer that this takes attention away from carefully modeling our thinking. Immediately, students got right to work: Students Trying Multiple Strategies. I loved watching one student explain how she Decomposed 6x5=2(3x3)+2(3x2). This same student struggled with this concept a few days ago. Her understanding has of decomposing and modeling a multiplication expression has clearly grown! By the time we were finished with this problem, almost all students had Multiple Strategies for 6 x 5.
Task 2: 36 x 5
During the next task, 36x5, I worked closely with a student who struggles with math: Supporting a Struggling Student. To help him understand how to decompose the 36, I showed him 16 = 10 + 6 and asked him to decompose 26 and then 36. This really helped. Then, I drew an array and asked him to use the array to solve 36 x 5. When we got to 5 x 10, I modeled a simpler problem, 1 x 10, and then asked him to solve 2 x 10... 3 x 10... all the way up to 5 x 10. During our share time, he then shared his work with the class: A Proud Moment!.
Task 3: 136 x 5
When solving 136 x 5, some students decomposed one multiplicand while others decomposed both the 136 and the 5: 136x5.
Task 3: 2136 x 5
During the final task, I asked a student to Explain Another Student's Work. This was a powerful experience and was incredibly validating to the other student! Again, students showed Multiple Strategies for 2136x5 on their white boards. Talk about developing number sense!
To begin, I invited students to get their math journals and meet me on the carpet. I then introduced the Goal: I can represent numbers in written form. Throughout this lesson, I will use the terms "written form" and "word form" interchangeably as I want students to view them as synonymous terms.
Forms of Numbers:
I explained: Do you remember yesterday when we talked about the three basic ways to represent numbers? The first way is called standard form. I presented the poster for Standard Form. Next, we have Expanded Form, and the last form is called Word Form. Prior to the lesson, I created each of these posters knowing that we could refer to them the rest of the year.
When reviewing expanded form, I wanted to deepen student understanding of expanded form by using four different colored strips of paper (similar to arrow cards) to show 2000 (green paper) + 500 (red paper) + 30 (yellow paper) + 2 (pink paper). This Expanded Form Demonstration really helped many students grasp the idea of expanded form. Some students responded, "Oh! Now I get it!"
Once we got to word form, I explained: Word form is a way to write numbers using words. For example, 2,532 would be written this way: two thousand, five hundred thirty-two. When teaching students how to write numbers in word form, there are three key concepts I always try to cover: 1. comma placement, 2. spelling of numbers, and 3. hyphen placement.
1. Comma Placement
To teach students the proper way to place commas in a number, I used following place value magnets to demonstrate comma placement on the board: Place Value Magnets & Comma Placement. I explained: Whenever we write numbers, we use commas to separate the periods in the place value chart. For example, we use a comma to separate the millions and thousands period. We also use a comma to separate the thousands and ones period. Here's an example: We would write 2,500,003 with two commas: two million, five hundred thousand, three. So if we just have 500,003, we only need one comma: five hundred thousand, three.
2. Spelling of Numbers
We then moved on to the spelling of numbers. I showed students the Spelling of Numbers Chart I had created prior to the lesson. I set high expectations by asking students to make sure every word is spelled correctly today!
3. Hyphen Placement
While looking at the Spelling of Numbers Chart, I asked students to observe which numbers have hyphens (or a dash). I asked questions to help students differentiate between numbers with a hyphen and numbers without: Does the number five have a hyphen? (no) How about the number eighteen? (no) Does sixty have a hyphen? (no) How about ten thousand? (no) Which numbers do have hyphens then? Students responded, "Only numbers like twenty-four." What other numbers require a hyphen? Student responses varied: "Sixty-six..." "Ninety-four... "Thirty-five..." Okay, so we use a hyphen with all numbers between 21 and 99, except with the multiples of 10, like thirty, forty, fifty...?
I knew students were ready to practice these concepts!
At this point, I asked students to create a three column in their math journals with the following headings: Standard Form, Expanded Form, and Written Form. I wanted to connect written form with prior learning. Here's what the chart will look like when we are finished with this activity: Standard, Expanded, Written Forms Chart.
1. Place Value Blocks:
2. Standard Form:
I then asked, What is the standard form for this number? Referring to the standard form poster, I asked: How would you write the number 2 using the digits 0-9? Students responded, "Just write 2!" I wrote the number 2 in the Standard Form column of the chart.
3. Expanded Form:
I continued: Let's look at the expanded form. Referring to the expanded form poster, I asked: How would you write 2 using the value of each digit? Students responded 2 in almost an annoyed way! They were anxious to be challenged! I always start with easy tasks and work up to more complex tasks to build a staircase of complexity!
4. Word Form:
Referring to the written form poster, I asked: How would you write the number 2 using words? One student said, "T...w...o."
More Complex Numbers
Students were clearly ready to move on to more difficult tasks! One step at a time, I continued building the learning progression. We continued the same steps: 1. Place Value Blocks, 2. Standard Form, 3. Expanded Form, and 4. Written Form using the numbers listed below.
I gradually released responsibility by asking students to complete their own charts in their student journals and to turn and talk with a partner before discussing the forms of each number as a class. I also used similar digits to reinforce number sense (112 = 12 + 100 more).
Flipping the Order of Tasks
For the last four tasks in the Standard, Expanded, Written Forms Chart, I provided the word forms for all four numbers at one time instead of modeling the number with place value blocks one at a time. This gave me more time to conference with struggling students. Also, I wanted to make sure students were able to interpret the written form of larger numbers.
As students finished, I asked for volunteers to complete the Standard and Expanded Form columns on the whiteboard in front of the class. Here, students explain the Standard & Expanded Forms for 72,072.. I ask questions to encourage student engagement and higher level thinking.
When writing the number, 522,004, some students struggled with representing a number with zeros. This student explained to the rest of the class how 522,004 would look if we interpreted it as 5,224: Understanding the Written Form for 522,004.
Next, students moved on to the Written & Expanded Forms for 800,008. When finished, the students at the board eagerly asked if they could complete the chart! I loved how excited they were to participate! Finally, students represented the Standard & Expanded Form for 905,602.
Base 10 Blocks
Before moving on to the final task, I wanted to give students the opportunity to represent the last four numbers in the Standard, Expanded, Written Forms Chart using the place value blocks on the board. I first lined up the Base 10 Blocks & Place Value Magnets. Also, I asked that students only look at the written form of each number.
The first student represented 72,072 using Base 10 Blocks perfectly. I absolutely loved watching this student show 800,008 using Base 10 Blocks. It was equally as amazing to watch another student "respectfully disagree" with him! Here, another student represents 905,602 using Base 10 Blocks perfectly again!
To ensure students were able to independently meet the goal of today's lesson, the final task was two practice pages (front to back) from the site below.
1. Practice Page #1:Writing Numbers for Word Names
2. Practice Page # 2: Writing Word Names for Numbers
During this time, I checked on each student and provided support and questioning as needed. Two students in particular needed extra support so I pulled them back up to the white board for individualized instruction. I'll address these students in the reflection section.
Most students finished within 15 minutes! I asked students to check their answers with peers. Peer-checking gives students the opportunity to practice Math Practice 3: Construct viable arguments and critique the reasoning of others. Here are examples of proficient students: Writing Numbers for Word Names and Writing Word Names for Numbers.