Diamond State Discovery Slides Diamond State Discovery
Grade 7 Math ATLAS Expedition
Proportions
Standard: 7.RP.A.2
Constant of Proportionality
y = kx
Ratio: \( k = y \div x \)
The Graph Rule
A straight line that passes through origin (0,0).
Hours (x) Cost (y) k 2 $5.00 2.5 5 $12.50 2.5 8 $20.00 2.5
Rational Numbers
Standard: 7.NS.A.3 Mastery
The Challenge:
\[ -4.5 + 2 \frac{1}{2} - (-3) \]
Pro Tip:
Use decimals for halves and fourths to avoid fraction math!
Step-by-Step Solve
1 \( 2 \frac{1}{2} \rightarrow 2.5 \)
2 \( -(-3) \rightarrow +3 \)
3 \( -4.5 + 2.5 = -2 \)
4 \( -2 + 3 = 1 \)
Circle Geometry
7.G.B.4 Relationships
Circle Formulas
Circumference: \( C = \pi d \)
Area: \( A = \pi r^2 \)
\( \pi \approx 3.14 \) or \( \frac{22}{7} \)
Diameter trap: Divide by 2 to get the radius \( r \) before finding the Area!
r = 5 ft
Angle Relations
Standard: 7.G.B.5
Complementary
Sum = 90°
Supplementary
Sum = 180°
Vertical
Always Equal!
Probability
7.SP.C.5 & 7.SP.C.6
Likelihood Scale
0 (Impossible)
0.5
1 (Certain)
Predictions
P(Event) × Total Trials
Arkansas Bag O' Gems
Bag: 12 Diamonds, 18 Quartz, 10 Jasper.
Total count: 40
P(Diamond): 12/40 = 0.3
P(Quartz): 18/40 = 0.45
ATLAS Practice
Multi-Select Mastering
Select ALL expressions equivalent to: \[ -0.75 - \left(-\frac{1}{2}\right) \]
\( -0.75 + 0.5 \)
\( -0.25 \)
\( -1.25 \)
\( -\frac{3}{4} + \frac{1}{2} \)
ATLAS Ready!
Check ALL Bubbles
Multi-select means checking every option! 1, 2, or even ALL might be right.
Equation Entry
Practice typing fractions and negatives on the keypad carefully before submitting.
NATURAL STATE STRONG!
Diamond State Discovery Worksheet Diamond State Discovery
Grade 7 Math ATLAS Prep expedition
Student:
Date:
Expedition 1: Proportions
1. At the Crater of Diamonds, 4 adults pay $52.00. Which equation represents total cost \( c \) for \( a \) adults?
A. \( c = 4a \)
B. \( c = 13a \)
C. \( a = 13c \)
D. \( c = 48a \)
2. Gem Rates over Time
Hours (\( x \)) Gems (\( y \)) 2 5 5 12.5
\( k = \)
Eq:
Expedition 2: Rational Numbers
3. Fayetteville temperature dropped \( 2.5^{\circ}\text{F} \) each hour for \( 3.5 \) hours, then rose \( 4.25^{\circ}\text{F} \). Find the net change. Show all steps.
Net Change: _______________
4. Select ALL expressions equivalent to \( -0.75 - \left(-\frac{1}{2}\right) \).
\( -0.75 + 0.5 \)
\( -0.25 \)
\( -\frac{3}{4} + \frac{1}{2} \)
\( -1.25 \)
Expedition 3: Geometry
5. Circular Pool Area
Diameter = 14 ft. Find Area using \( \pi \approx \frac{22}{7} \).
Area = ____________ \( \text{ft}^2 \)
6. Angle Solve
Complementary: \( (3x + 10)^{\circ} \) and \( 50^{\circ} \).
\( x = \) ________
Expedition 4: Probability
Bag contents: 15 Honeybees, 20 Mockingbirds, 15 Apple Blossoms (50 Stickers Total)
Part A: Individual Probability
What is the probability of picking an apple blossom? (Express as decimal )
P =
Part B: Group Prediction
If you buy 200 stickers, how many would you predict to be mockingbirds?
Prediction: _______________ mockingbirds
Diamond State Discovery • Grade 7 Math ATLAS • Page 2 of 2
Discovery Guide Teacher Resource Discovery Guide
Teacher Resource • Grade 7 Math ATLAS Prep
Learning Objectives
Analyze proportional relationships in tables and equations (7.RP.A.2).
Solve multi-step problems with mixed rational numbers (7.NS.A.3).
Calculate area and circumference of circles (7.G.B.4).
Use probability models to make predictions (7.SP.C.6).
Pacing
Warm-up: 10m
Instruction: 25m
Guided Practice: 15m
Independent: 20m
ATLAS Strategy: The Natural State Way
The Rational Number "Pitfall"
In Grade 7, the biggest hurdle is combining multiple operations with signs. Strategy: Encourage students to "separate the sign from the size." Determine if the final answer will be positive or negative before calculating values.
"If you're at -2.5 and you drop 3.5 more, you're getting 'more negative'. Don't let the subtraction sign confuse you!"
Proportional Reasoning
Students often struggle to identify the constant of proportionality (k) in word problems. Strategy: Use the "Unit Rate Anchor." If 4 adults cost $52, find what 1 adult costs. That is your k .
"k is just the price for ONE. One diamond, one ticket, one mile."
Misconception Minefield
Circle Area vs. Circumference
Students frequently use d (diameter) for area or forget to square the radius. Fix: Create a visual: "Area is inside (square units like tiles), Circumference is around (like a fence)."
Probability as "Likelihood"
Students may think a probability of 0.5 means something is "unlikely." Fix: Reinforce that 0.5 is exactly "equally likely" and anything above 0.5 is "likely."
ATLAS Question Style Guide
Hot Spot
Clicking specific points on a graph or number line.
Multi-Select
Choosing multiple correct answers from a list.
Equation Entry
Typing numerical values or algebraic expressions.
Discussion Starters
"How does changing the radius of a circle affect its area compared to its circumference?"
"If a probability is 0.75, does that mean exactly 75 out of 100 trials MUST be successful?"
Discovery Key Answer Sheet Discovery Key
Answer Sheet & Scoring Guide
Arkansas Math Grade 7
Expedition 1: Proportions
1
Answer: B \( (c = 13a) \)
Teacher Note (7.RP.A.2):
Unit rate \( k = 52/4 = 13 \). Constant ratio \( y/x \) defines proportionality in Grade 7.
2
Answer: \( k = 2.5 \); Eq: \( y = 2.5x \)
Work: Check all points: \( 5/2 = 2.5 \), \( 12.5/5 = 2.5 \), \( 20/8 = 2.5 \).
Expedition 2: Rational Numbers
3
Answer: \( -4.5^{\circ}\text{F} \)
Pedagogical Note (7.NS.A.3):
Students often fail to attach signs correctly. "Drop" is negative. Calculation: \( 3.5 \times (-2.5) + 4.25 = -8.75 + 4.25 = -4.5 \).
4
Multi-Select (Select ALL 3 Correct):
\( \checkmark \, -0.75 + 0.5 \)
\( \checkmark \, -0.25 \)
\( \checkmark \, -\frac{3}{4} + \frac{1}{2} \)
Expedition 3: Geometry
5
Answer: \( 154 \text{ ft}^2 \)
Work: \( r = 7 \). \( Area = (22/7) \times 7^2 = 154 \).
6
Answer: \( x = 10 \)
Work: \( (3x + 10) + 50 = 90 \rightarrow 3x + 60 = 90 \rightarrow 3x = 30 \rightarrow x = 10 \).
Expedition 4: Probability
7
Part A: 0.3
Work: \( 15 \div 50 = 3 \div 10 = 0.3 \).
Part B: 80 Mockingbirds
Work/Prediction: \( (20/50) \times 200 = 80 \).
ATLAS Assessment Scoring
Questions like Item 4 are often worth 1 point with no partial credit for selecting fewer than all correct choices.
