Sunday, September 28, 2014

Teaching for Mastery: 5th Grade Coordinate Grid Week

This is coordinate grid week. It's also the first week of the year when we're ready to tackle unit standards with a learning sequence, a sequence we'll apply to later units.

Since this is the first time I've taught the new CCSS fifth grade standards, working through each unit takes lots of time and attention. I will apply a similar sequence of events to each unit.

1. Whet Their Appetite, Make it Meaningful
We'll take a look at the aerial photo of the playground.

I'll say, can anyone locate the "back swing set." I'm sure hands will raise quickly, and I'll let students describe where it is. I imagine they'll say things like "in the back," "next to the trees," and "far from the building."  I'll write their words down, and underline the location words such as "next to," "far from," and "in the back."

After that I'll explain that mathematicians aren't satisfied with vague descriptors since they like their descriptions to be precise and exact. Math brings order and organization to our world, and that helps us to see patterns and determine relationships.

One way to order or organize a map is to overlay the map with a coordinate grid. Then I'll show the coordinate grid map overlay and explain how using the grid provides us with a set of steps with which to see the map and talk about it.

I'll pass out the grid map to all and we'll identify the vocabulary.
Link for Handout

We'll complete the worksheet, graph a few significant ordered pairs on the school map, then practice making a picture with ordered pairs.

Finally, at the end of the lesson, we'll review the vocabulary with this catchy Flocabulary rap.

2. Provide Opportunities for Review and Study for Homework
I will encourage students to sing the Flocabulary rap for homework. I'll also ask them to practice drawing a number of pictures using ordered pairs and practice the concepts using Khan Academy.

3. Roll out the unit with review, practice, and new learning. 
The next day we'll review the unit standards in student language (see below). Then I'll pass out the Flocabulary lyrics and we'll revisit the song. Together we'll solve some real-world problems by graphing points and interpreting values.

On Wednesday, students will review measurement conversions, study sequences, and generate terms related to measurement.

Thursday will find us using Khan Academy's great example of using coordinate grids to find the relationship between two sequences.

4. Master with Application, Content Creation, and Share. 
Finally, on Friday students will use their new knowledge to create their own real-world problems (using measurement information) that can be solved and/or interpreted on a coordinate grid. Application of the new information in a meaningful way is the best way to master the content. I will share that activity when we get there.

5. Unit Review, Study, and Assessment
Next week students will review all standards related to our first math unit of the year. I will teach students multiple ways to study for an assessment in order to learn the material well.

As I've stated before there's a temptation to rush the standards and the teaching/learning year, but if we do that, students won't establish important routines and dispositions that lay the foundation for engaged, successful math learning and thought. I'll make the time to reach all standards, but we'll do it in a thoughtful, student-centered way.

The standards in student language:

Coordinate Grid Learning Standards:
Monday and Tuesday:
  1. I will understand the math vocabulary related to coordinate grids.
  2. I will graph or plot ordered pairs (coordinates on the grid) with precision.
  3. I will represent real world problems by graphing points, and interpret coordinate values of the points in the context of the situation.
  1. I will generate terms in a sequence.
  1. I will graph sequences on a coordinate grid.
I will observe the relationship between the terms in one sequence and the terms in another.

CCSS Standards Language:
  • 5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate)
  • 5.G.A.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
  • 5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.