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1.1 — Checkerboard Borders
Human review completed .
Describe a counting method with numbers, then use a variable to make the method work for different-sized squares.
1. In class: A Develop Understanding Task
Work through “Checkerboard Borders,” Main A–B, on pages 1–2 of your MVP packet with your class.
2. Ready — Check equation solutions and complete ordered pairs
What makes a number a solution?
A solution makes an equation true. To test a proposed solution, substitute it: replace the variable with that number, use parentheses for negative numbers, and calculate both sides. You do not need a new equation-solving method to choose among the packet’s candidates.
Worked example — Ready 2
Original problem: For \(8-2b=-2\), choose \(b=-3\), 0, or 5.
Try \(b=-3\):
The result is not −2, so −3 does not work.
Try \(b=0\):
The result is not −2, so 0 does not work.
Try \(b=5\):
This matches the right side. Answer: \(b=5\).
An ordered pair records an x-value and a y-value
In \((x,y)\), the first number is the \(x\)-value and the second is the \(y\)-value. To complete a pair, substitute the given \(x\) into the equation and calculate \(y\).
Worked example — Ready 6
Use the equation \(y=-4x+9\) to complete the ordered pair when \(x=-5\).
Substitute −5 for \(x\):
Write the x-value first and the y-value second:
The order matters: \((-5,29)\) and \((29,-5)\) name different points.
Try each problem before opening the key.
Check your work — Ready 1–8
| Problem | Answer | Check |
|---|---|---|
| 1 | \(x=2\) | \(3(2)+7=13\) |
| 2 | \(b=5\) | \(8-2(5)=-2\) |
| 3 | \(a=-3\) | \(5+4(-3)+8=1\) |
| 4 | \(t=10\) | \(6(10)-5+5(10)=105\) |
| 5 | \((8,33), (-1,-21), (5,15)\) | |
| 6 | \((-5,29), (2,1), (4,-7)\) | |
| 7 | \((-4,-9), (0,-1), (7,13)\) | |
| 8 | \((-9,18), (1,8), (5,4)\) | |
3. Set — Complete tables with a constant change
Check your work — Set 9–12
Values below correspond to inputs 1, 2, 3, 4, 5, 6, 7, in that order. All amounts are dollars.
| Problem | Table values | Explanation |
|---|---|---|
| 9 | 605, 610, 615, 620, 625, 630, 635 | Start with 600; add 5 for each birdhouse. |
| 10 | 485, 470, 455, 440, 425, 410, 395 | Start owing 500; subtract 15 after each monthly payment. |
| 11 | 10, 20, 30, 40, 50, 60, 70 | Add 10 after each weekly deposit, starting with no savings in this model. |
| 12 | 35, 45, 55, 65, 75, 85, 95 | Start with 25; add 10 after each week. |
4. Go — Plot ordered pairs from a table
Check your work — Go 13–16
13
\((0,3),\ (2,7),\ (3,9),\ (5,13)\)
14
\((0,14),\ (4,10),\ (7,7),\ (9,5)\)
15
\((2,11),\ (4,10),\ (6,9),\ (8,8)\)
16
\((1,4),\ (2,7),\ (3,10),\ (4,13)\)
Additional learning resources
| Resource | What it helps with and scope |
|---|---|
| Khan Academy — Writing basic expressions with variables | Review translating words into expressions. Simpler than the border task; useful for understanding what a variable and operations represent. |
| Khan Academy — Checking ordered pair solutions to equations, example 1 | Substitute coordinates to check an equation. Supports Ready; checks a complete pair rather than filling in a missing output. |
Teacher/parent review of the source packet
The main task accepts different valid counting strategies.
Coverage
| Packet component | Support |
|---|---|
| Main A–B · pages 1–2 | Complete in class using the source packet; no additional worked solution here. |
| Ready 1–8 · page 3 | Substitution, checking solutions, ordered-pair explanation and complete key. |
| Set 9–12 · page 4 | Answer key with all table values and explanations. |
| Go 13–16 · page 5 | Answer key with four checking graphs showing every supplied point. |
Prompts and data adapted from Mathematics Vision Project, Secondary Mathematics I, Module 1 student packet, Section 1.1, pages 1–5, licensed under CC BY 4.0. Explanations and diagrams prepared for this supplement.
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