Jennifer Valentine GALLEGO BASIC ELEMENTARY SCHOOL, TUCSON, AZ
3rd Grade Math : Unit #7 - Rounding : Lesson #2

Rounding to the Hundred's Place

Objective: SWBAT round to the nearest hundred by evaluating the place value and relationships of numbers.
Standards: 3.NBT.A.1 3.NBT.A.2 MP1 MP2 MP5
Subject(s): Math
60 minutes
1 Overview for the Teacher - 0 minutes
2 Finding the Halfway Point between Hundreds - 24 minutes

This is an abstract, two-step process and one with which they need specific, straightforward practice.  

I directly teach the following examples. As I draw the number lines, I explicitly talk through each step.  I count up to the halfway point by tens, mark the halfway point, and reiterate that from that halfway point on we round up to the next number.  Depending on the needs of the group I might teach fewer or more examples than those listed below.  

 halfway/midpoint  (hundreds)

600  and 700

1400 and 1500

 

7700  and 7800

 

11,200  and 11,300

20,000 and 20,100

 

33,400 and 33,500

 

600,000 and 600,100

820,200 and 820,300

 

550,500 and 550,600

 

Based on what I observed during the guided practice, I give them one of 3 short practice pages on finding the halfway point between two hundreds.  I collect the practice pages and review them after school to determine how to differentiate in the next lesson.  I often spend two days on this lesson as well.  

Midpoint Between Hundreds (extra support)

Midpoint Between Hundreds (on level)

Midpoint Between Hundreds (above level)


3 Rounding to the Hundred's Place (Guided & Independent Practice) - 30 minutes

After we've practiced identifying the halfway point between two hundreds, I reteach the skill of finding the hundred before/after the number they are given to round. 

I directly teach counting down and up to the closest hundred for the following examples because I have found some students do not identify the closest hundred.  For example, for the number 1234, some students may identify 1000 and 1300 as the closest tens.  

I do not require students to Mark the Ten Intervals if they don't need to, but many of them find it helpful.

835, 487, 65, 2430, 5287, 2455, 9,502,  11,283,  14,900

 Based on what I observed during the guided practice, I give them one of these three short practice pages on rounding to the closest hundred.  

Rounding to Closest Hundred (extra support)

Rounding to Closest Hundred (on level)

Rounding to Closest Hundred (above level)

I give my students one of these tasks, but instead of using the papers I wrote the numbers up on the board, labeled them group A, group B and group C, and had them copy the problems onto lined paper.  I made sure they left enough space between their number lines.

I place most kids in a group based on what I'd observed in their work. For those students I wasn't sure about where they belong, so I let them choose.  I also tell them that if I'd placed them in a group that didn't seem like it was the right level for them to learn (either too difficult or too easy) that they could switch themselves.  Nobody asks to switch, but several children ask if they can do another level once they finish the assigned one.  Of course I say yes!  

The advantage to doing this using the work pages is that student errors from copying are eliminated.  Also, perfectionist students don't spend an interminable amount of time making straight number lines and children with handwriting difficulties aren't pulled off track by all the writing.  Finally, the scaffolded pages above have part of the number line completed.  In my classroom, I had to call this group over and do those parts with them.

The advantage to doing it on scrap paper is that I can easily adjust a child's level at any time by switching them to a different list or giving them completely different numbers.  I have two children who have completely mastered this skill.  To be certain, I give them ridiculously large numbers to make sure they can still do and explain their work.  They can.

 

4 Exit Ticket - 7 minutes

Ask children to either write or be prepared to verbally explain their answer to these questions:

How is rounding to the hundred's place similar to rounding to the ten's place?  How is it different?  Do you find one easier than the other?  Explain why or why not.

5 Qualitative Notes on Student Progress - 1 minutes

I can't always take detailed notes but I make a point to take the time to do so at least once a week for each student.  When I'm creating lessons, I break down the standard into the smallest components and plan to address each of those components.  The same list I use for planning, creating and revising lessons can work as a student checklist, as I know each of these smaller tasks will be addressed in the unit.  I find it helpful to type up quick notes about student errors because these help me plan reteaching and extension and their errors can also inform me about what I can improve in delivering the content.  This is an example of notes I took during this unit on rounding.  

I keep these notes in mind during tomorrow's lesson, Stories in Stone, in which the rounding practice is embedded in geology content.

Task Analysis in Lesson Planning
Lesson Planning

Task analysis is at the core of my lesson planning.  If students don't understand something, I break the problem/question/task down into its constituent parts to determine subcomponent is tripping them up.  Sometimes it's one piece, sometimes it's many pieces, but unless I'm aware of all the different parts of a given skill/concept, I can't effectively reteach.  I've learned over the years that there are many places where students experience confusion related to rounding and in planning this lesson I'm addressing two of them:

  • Finding the midpoint between two given numbers (hundreds).
  • Finding the two hundreds closest to the target number (if they are confused, I step them back to counting by ones to reach the closest hundred in either directions). 

 

This focus on the sub-skills allows me to more effectively eliminate student misunderstandings and teach them all the necessary steps in this process.  Some students may not need the sub-skills, but more often than not they do, at the very least, need an overview.