## Reflection: Diverse Entry Points The Number Line Project, Part 2: Two Dimensional Number Lines - Section 4: Part 2: Work Time and Next Steps

In a class where all students have demonstrated strong arithmetic skills, I'll have them race the clock.  "I've seen students complete this assignment in under four minutes," I'll say about the first addition table.  "See how quickly you can get it done!"

Whether they're racing the clock or not (the brightest students will say that it's just a physical feat, of how fast you can write 210 numbers) this is not really about addition!  It's about patterns.  It's impossible to emphasize this point too much with kids - that's what this whole assignment is about.

Some students will ask if they're right on the multiplication tables.  When they do, I show them how patterns can be used to check their work.  Every column and every row is counting by a certain number.  Uncertain students can make sure that each of these pattern is increasing by the same amount with each successive term.  Furthermore, if a pattern increases from left to right, then we can also say that it decreases from right to left.  This logic can be employed when students are wondering what to do about the products in the second, third, and fourth quadrants on the back of Part 2b.  Because all students are working at their own pace, there are ample opportunities to have conversations like these with individuals and small groups.  As I often do, I'll rely on students to share their expertise among each other, and I will often refer one student in need of help to another who can offer it.

Here, we are going to back to some of the work we did with patterns in previous weeks.  As we return to patterns problems next week and beyond, this multiplication table will help.

Accommodations and Conversations
Diverse Entry Points: Accommodations and Conversations

# The Number Line Project, Part 2: Two Dimensional Number Lines

Unit 2: The Number Line Project
Lesson 4 of 9

## Big Idea: The mathematical structures we build today will be used to justify many algebraic ideas in the coming months.

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Subject(s):
Math, Measurement, modeling, Number Sense and Operations, proportional relationships, transformation, equation, graph
43 minutes

### James Dunseith

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