Teaching
Classroom Management
Cooperated
Gradual Release
Example: TEKS 6.3D Add and Subtract Integers
I Do (Teacher Models)
Teacher says:
“Let’s add two integers with different signs, −3 + 5. I’ll start at −3 on the number line. Since we’re adding a positive 5, I move 5 units to the right. Where did I land?”
Students respond: “2!”
“Yes! So, −3 + 5 = 2. Quick check — thumbs up if your sum was positive, thumbs down if you think it’s negative.”
“Yes, the sum is positive because the absolute value of 5 is greater than the absolute value of −3.”
Teacher then models subtraction:
“Now let’s subtract two integers with the same sign, 6 − 9. That’s like adding two integers with different signs, 6 + (−9). Starting at 6, I move 9 units left. Where did I land?”
Students respond: “−3!”
“Yes! So, 6 − 9 = −3. Quick check — thumbs up if your sum was positive, thumbs down if you think it’s negative.”
“Yes, the sum is negative because the absolute value of 9 is greater than the absolute value of 6.”
Students watch and take notes.
We Do (Guided Practice)
Teacher and class solve together:
“Let’s add two integers with the same sign, −4 + (−7) together. Everyone point to −4 on your number line.”
Now we’re adding a negative 7. In which direction should we move?”
Students respond: “Left!”
“Yes! Let’s move left 7 spaces together. Where did we land?”
Students respond: “−11!”
“Yes! So the answer is −11. Quick check — what happens to the sign of the sum when we add two negatives?”
Teacher calls on students to explain each step while providing support.
You Do (Independent Practice)
Students work independently on similar problems, for example:
−8 + 3 = ?
5 − 9 = ?
−2 + (−6) = ?
Teacher circulates and checks for understanding.
Exemplar
Definition
An exemplar is
A model example that demonstrates mastery of a math skill, concept, or problem-solving process.
It can be
A teacher-created example (like a perfectly worked-out solution showing all reasoning steps)
Or a student’s work sample that meets or exceeds the learning goal
Exemplars Often Show
Clear steps for solving a problem (e.g., showing the model, equation, and explanation)
Mathematical reasoning (students justify why their answer makes sense)
Correct use of vocabulary (e.g., integers, ratio, quotient)
Neat organization and labeling
Connections between models and equations (e.g., showing how a number line relates to integer rules)
Example (TEKS 6.3D — Add and Subtract Integers)
Exemplar Student Work:
Problem: −6 + 9 = ?
Step 1: Start at −6 on the number line.
Step 2: Move 9 spaces to the right (because we’re adding a positive).
Step 3: Land on 3.
Answer: −6 + 9 = 3
Explanation: “When adding a positive, move to the right. The sum is positive because the number with the larger absolute value is positive.”
This exemplar shows mathematical accuracy, clear reasoning, proper vocabulary, and a visual model with written explanation.
How Teachers Use Exemplars
Before the lesson: Show an exemplar to set expectations (“Here’s what a strong answer looks like”).
During the lesson: Model thinking using an exemplar (“Notice how I explain why I moved right on the number line”).
After the lesson: Use exemplars to guide feedback (“Your answer was correct, but your explanation didn’t match the exemplar level yet”).
Why Exemplars Matter
Build clarity about expectations
Encourage self-assessment and peer feedback
Support struggling learners by giving a visual and concrete goal
Anchor rubrics and success criteria
Exemplar: Prime Factorization
Problem: Find the prime factorization of 60.
Exemplar Solution (Model Work)
Step 1: Start by dividing by the smallest prime number possible.
60÷2=30
Step 2: Continue dividing by prime numbers.
30÷2=15
Step 3: 15 is not divisible by 3, so we move to the next prime: 3.
15÷3=5
Step 4: 5 is a prime number, so we stop here.
Prime factors:
60=2×2×3×5
or in exponent form:
60=(2^2)×3×5
Written Explanation (Student Voice Example):
“To find the prime factorization of 60, I divided by the smallest prime, 2, until I couldn’t anymore. Then I divided by 3, and finally got 5, which is prime. The prime factors of 60 are 22×3×52^2 × 3 × 522×3×5. I checked my work by multiplying them: 2×2×3×5=602 × 2 × 3 × 5 = 602×2×3×5=60, so it’s correct.”
Factor Tree Model (Visual)
60
/ \
2 30
/ \
2 15
/ \
3 5
Prime Factors: 2, 2, 3, 5
Answer: 60=2^2×3×5
Teacher / Peer Discussion Prompts:
“Why do we only use prime numbers in the factorization?”
“How can we check that our factorization is correct?”
“What would happen if we started with 3 instead of 2?”
“Does the order of factors change the product?”
Why This Is an Exemplar
✅ Shows all steps clearly
✅ Uses a visual model (factor tree)
✅ Includes explanation and reasoning
✅ Checks the answer by multiplying back
✅ Uses proper mathematical notation