15.2 Constructed-Response Exercise 1: Numeracy

What the Exercise Actually Asks

Exercise 1 is titled Numeracy. Its introduction screen states: "In this exercise, you will use your knowledge of numeracy skills and instruction for students with exceptional needs. You will be asked to respond to one prompt." The rubric is derived from Standard VIII (Curriculum and Instruction) and Standard X (Instructional Resources), and you have 30 minutes.

The introduction screen also publishes the Criteria for Scoring, which is a literal checklist of what the highest rubric level requires. To satisfy Level 4, the response must provide clear, consistent, and convincing evidence of:

1. a brief description of a student with exceptional needs with whom you will be working;
2. a description of one important concept or skill regarding a topic related to numeracy;
3. a thorough description of two instructional activities and two instructional resources you would use to teach this concept or skill to the student you describe; and
4. a thorough, in-depth explanation of how these activities and resources would be particularly effective for the student you describe and how you would measure the student's success.

The published sample prompt narrows the topic: "You will be teaching a mathematics lesson on measurement to a student with exceptional needs." It then repeats the four criteria as prompt bullets, adding that the student description should include age/grade level/developmental level, exceptionality, and strengths/needs, and that the resources should include "any applicable technological resources."

Two structural facts follow immediately. First, you invent the student — this is a hypothetical drawn from your own experience, not a supplied case file, so nothing stops you from preparing one in advance. Second, the numbers are fixed: two activities, two resources. Official guidance is explicit that assessors evaluate only the number of examples requested, so a third activity is unscored text that cost you minutes.

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The Four Rubric Levels, in the Exercise's Own Words

Read the Level 3-to-4 boundary carefully, because it is where most candidates lose points. Both levels contain all four elements. The difference is thorough, in-depth, and particularly effective for the student you describe. Level 4 is earned by tying every choice back to the specific learner profile you wrote in your first paragraph — not by adding more strategies.

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A Reusable Response Architecture

Use headings that mirror the criteria. Assessors are locating evidence against named criteria; making it findable costs nothing and saves them nothing but time.

Exercise 1 response skeleton (30 minutes)

  0:00-0:03  THE STUDENT
             Age / grade / developmental level, exceptionality,
             2 strengths, 2 needs relevant to numeracy
  0:03-0:06  THE CONCEPT OR SKILL
             ONE bounded idea + why it matters in the progression
  0:06-0:16  INSTRUCTIONAL ACTIVITY 1 ... ACTIVITY 2
             What the student does, what I do, what the sequence is
  0:16-0:21  INSTRUCTIONAL RESOURCE 1 (material) ...
             RESOURCE 2 (human or technological)
  0:21-0:27  WHY THESE FIT THIS STUDENT
             Each choice tied to a named strength or need
  0:27-0:30  HOW I MEASURE SUCCESS
             Instrument + criterion + schedule + decision rule

Paragraph 1 — the student (3 minutes, and rehearsed in advance)

Prepare two or three flexible profiles before test day: for example, a kindergartner with a developmental delay, a fourth grader with a specific learning disability in mathematics, and a secondary student with a moderate intellectual disability. Each should have two concrete strengths and two concrete needs written in numeracy-relevant terms. A usable profile reads like this:

Maya is a 9-year-old fourth grader identified with a specific learning disability in mathematics calculation. She has strong oral language and reasons well about real situations, and she persists when she can see her own progress. Her working memory for multi-step procedures is weak, and her understanding of length measurement is built on reading tick marks rather than on units, so she aligns objects at the "1" mark and reports lengths one inch too long.

That last sentence is doing enormous work: it makes the concept selection inevitable and gives every later choice something to attach to.

Paragraph 2 — one important concept or skill (3 minutes)

Name one bounded, teachable idea and state where it sits in the numeracy progression. "Unit iteration — that measuring length means counting equal-sized units placed end to end with no gaps or overlaps, beginning at zero" is a concept. "Measurement" is a topic, and "improving math skills" is not scorable. The Level 2 descriptor explicitly anticipates concept descriptions that "contain misconceptions or misinformation," so precision here is cheap insurance.

Paragraphs 3–4 — two activities (10 minutes)

An instructional activity describes what the student does, what you do, and in what sequence. Extended time, preferential seating, and "hands-on learning" are not activities — the first two are accommodations and the third is a category. Strong activities name the materials, the teacher moves, and the cognitive work:

Activity 1 — Contrasting iteration. Maya measures the same paper strip twice with linking cubes: once placed carefully end to end, once with visible gaps. She records both counts, and I ask her to explain why the same strip produced two answers. I model the think-aloud once, then fade to questioning. This makes the unit, not the numeral, the object of her attention.

Activity 2 — Building a ruler. Maya iterates a single one-inch unit strip along a paper tape, marking each endpoint and then labeling the marks. Because she builds the tool, she sees that "1" labels the end of the first unit and that measurement starts at zero. She then measures four classroom objects with her own ruler and with a standard ruler and compares results.

Paragraph 5 — two resources (5 minutes)

Standard X defines resources as "both human and material." Pairing one material and one human or technological resource demonstrates the standard's full scope:

Resource 1 (material) — linking cubes, one-inch unit strips, and a large demonstration ruler and number line, so the iteration is physically externalized rather than held in working memory.

Resource 2 (human/technological) — a trained peer partner using a scripted prompt card ("Where does your unit start? Any gaps?"), plus a virtual manipulative ruler app that snaps units end to end and reports the count, multiplying practice opportunities with immediate corrective feedback without requiring me at her elbow.

Paragraph 6 — why these are particularly effective for this student (6 minutes)

This is the paragraph that separates Level 3 from Level 4. Tie each choice to a named feature of the profile: the contrast activity targets her specific tick-mark misconception rather than drilling the procedure that encodes it; the physical and virtual manipulatives offload the working-memory demand she cannot meet; the peer partner and the app exploit her responsiveness to visible progress; building a permanent ruler artifact gives her something to return to when the procedure decays.

Paragraph 7 — how you would measure success (3 minutes)

Name an instrument, a criterion, a schedule, and a decision rule:

I will administer an eight-item criterion-referenced measurement probe — four items aligned at zero, four requiring alignment from a non-zero start — at baseline and then weekly, graphing correct measurements. Mastery is 7 of 8 correct across two consecutive probes. On one item per probe I will ask her to show me how she measured, to confirm she is iterating units rather than reading marks. If four consecutive points fall below the aimline, I will return to non-standard unit iteration before continuing with standard tools.

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The Failure Modes Assessors See Most

Practise this exercise the way NBPTS recommends practising all three: set a timer for 30 minutes, write a full response, then score yourself against the four criteria bullets line by line. If you cannot point to the sentence that satisfies each bullet, an assessor will not find it either.