MCT Demo — Teacher Dashboard

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This lesson is a critical juncture for your class

MCT assessed 26 students with a diagnostic interview: an anchor task (1/2 + 1/5), a transfer task (2/3 + 1/4), and prerequisite probes when needed. Average interview: 7.2 minutes. 10 of 26 students will enter today with misconceptions that directly interfere with Activities 1 and 2.

Student Reasoning Map · Fraction Addition

L0

No partitioning

Marcus J.

L1

Halves only

Destiny W. Amira K.

L2

"Add everything"

Sofia M. Ethan C. Fatima A. Noah B. Lily T. Omar H.

L3

Procedure only

Isabella G. Liam P. Aisha N. Tyler K. Zara M. Jaylen

L4

Equivalence

Emma R. Carlos D. Maya S.

L5

Flexible

Jackson W. Chloe L. Leo F.

L6

Fluent

Olivia H. Nia J. Ryan T. Sophia C. Ben K.

Warm-Up How Many Do You See? Sofia's group will count squares but won't connect to fraction ops 10 to watch ▾

Core Finding Common Denominators Highest risk. "Add everything" group will apply their broken algorithm 6 at risk ▾

What the Lesson Does

Students find values of 2/3 + 1/4 and 2/9 - 1/6 where neither denominator divides the other. IM monitors for multiples strategy vs. product strategy.

What MCT Found

"Add everything" group will apply "add numerators, add denominators" and get 3/5 for 2/3 + 1/4. Consistent but wrong. Confident.

Sofia M. Ethan C. Fatima A. Noah B. Lily T. Omar H.

Procedure-only group will get correct answers but can't explain why common denominators work. All said "that's the rule."

Isabella G. Liam P. Aisha N. Tyler K. Zara M. Jaylen

MCT Adaptation

For the "add everything" group: hand them the warm-up area diagram alongside the expression. Ask them to write their answer first, then check against the diagram. The dissonance between "3/5" and "11/12" is the teaching moment. For the procedure-only group: ask Isabella or Jaylen to show on the area diagram where the twelfths come from.

If You See / Then Try

If you hear

"I got 3/5" or "2+1 is 3 and 3+4 is 5"

Then ask

"Is 3/5 bigger or smaller than 2/3 by itself?"

If you hear

"That's just the rule" when asked about common denominators

Then say

Point to area diagram: "Show me where the 12 comes from."

Core Denominator Strategies Well-matched for most. Pair solid students with procedure-only students Most ready ▾

Synthesis How Did You Decide? Listen for "that's the rule" answers. If you hear them, the gap persists Check understanding ▾

Prep Checklist for Lesson 10

1

Bring fraction strips (halves, thirds, fourths, fifths, sixths). Place a set at Marcus, Destiny, Jaylen, and Amira's tables.

2

Seat Sofia, Ethan, Fatima, Noah, Lily, Omar near each other so you can circulate quickly during Activity 1.

3

Plan pairs for Activity 2: Jackson + Isabella, Emma + Liam, Carlos + Aisha, Maya + Jaylen.

4

Print the warm-up area diagram for the "add everything" group to reference during Activity 1.

After Lesson 10 · Quick Check

Answer these after class. MCT will use your responses to adjust Thursday's Lesson 11 prep.

Did the "add everything" group use a common denominator in the Cool-Down?

If no → MCT will flag a 10-minute small-group pull at the start of Lesson 11

Could any procedure-only student explain WHY common denominators work (not just how)?

If no → MCT will add a "same-size pieces" visual to Thursday's warm-up, targeting Isabella, Jaylen, and Liam

Did Marcus or Destiny engage with the fraction strips during the warm-up?

If no → MCT will recommend fraction strips all week + peer mentor for Lesson 11

The loop: Diagnose (MCT interviews) → Adapt (today's lesson) → Verify (this check) → Plan (tomorrow's Lesson 11). MCT updates Thursday's prep automatically.