7.6 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Visual Models · Distance on the Coordinate Plane · Distance · Procedural Fluency

Name: Date: Period: Learning Goal:

■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do you find distance on the coordinate plane?

1If points are on the same side of zero, subtract; if they are on opposite sides of zero, add the absolute values.

Distance is how far apart two points are, and it is never negative. When two points share a row or a column, you can find the distance using their coordinates. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.

2Worked Example — Watch me

I will find the distance from (-3, 2) to (4, 2). Both have y = 2, so they sit on the same horizontal line.
The points are on opposite sides of zero, so I add the absolute values.
|-3| = 3 and |4| = 4.
I add: 3 + 4 = 7. The distance between them is 7 units.

3Mathematical Word Bank

Distance on the Coordinate Plane (Distancia en el plano de coordenadas) — The positive space between points, found from the absolute difference of coordinates on a horizontal or vertical line.
Distance (Distancia) — How far apart two points are. It is never negative.
Absolute value (Valor absoluto) — How far a number is from zero. It is never negative.
Horizontal distance (Distancia horizontal) — How far apart two points are going left or right.
Vertical distance (Distancia vertical) — How far apart two points are going up or down.
Coordinate plane (Plano cartesiano) — A grid with a line going across and a line going up to plot points.

4Watch out

A common mistake in Distance on the Coordinate Plane is subtracting the coordinates as if both points were on the same side of zero, instead of adding their absolute values when the points are on opposite sides. For example, to find the distance between (-6, 3) and (2, 3), a student might subtract 6 − 2 = 4, but since -6 and 2 are on opposite sides of zero, the absolute values must be added instead: |-6| + |2| = 6 + 2 = 8. The correct distance is 8 units, not 4. Before you submit, ask: 'Are these two points on opposite sides of zero — and if so, did I add the absolute values instead of subtracting?'

1 MULTIPLE CHOICE
Two points are at (-3, -7) and (-3, 5). What is the distance between them?
1. A12 units
2. B2 units
3. C7 units
4. D8 units
✏️ Workspace & Solution Steps
2 MULTIPLE CHOICE
What is the distance between (2, 3) and (2, 8)?
1. A11 units
2. B5 units
3. C6 units
4. D5.5 units
✏️ Workspace & Solution Steps
3 MULTIPLE CHOICE
What is the distance between (-4, 1) and (3, 1)?
1. A1 unit
2. B12 units
3. C7 units
4. D-7 units
✏️ Workspace & Solution Steps
4 MULTIPLE CHOICE
The Bank is at (2, 3) and the Library is at (2, 9). How many blocks apart are they?
1. A6 blocks
2. B12 blocks
3. C3 blocks
4. D11 blocks
✏️ Workspace & Solution Steps
5 MULTIPLE CHOICE
The Park is at (-4, 5) and City Hall is at (3, 5). How many blocks apart are they?
1. A1 block
2. B7 blocks
3. C12 blocks
4. D5 blocks
✏️ Workspace & Solution Steps
6 MULTIPLE CHOICE
The Café is at (-2, 1) and the Gym is at (-2, -4). How many blocks apart are they?
1. A3 blocks
2. B5 blocks
3. C6 blocks
4. D2 blocks
✏️ Workspace & Solution Steps

📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim

Starter: My mathematical claim is that the solution is...

E Evidence

Starter: The evidence from the model/table demonstrates that...

R Reasoning

Starter: This proves my answer because the standard mathematical definition of...

Student Mastery Self-Assessment:

1 · Need More Support

2 · Getting Closer

3 · Got It / Solid

4 · Master / Can Teach It