The response below is a fictional illustration, not an actual pupil record or a diagnosis. A short reteaching plan can connect objects, tens-and-ones language and written notation, then collect a separate independent response without inventing what the learner understood.
Prepare the original representation task
Use a clean tens/ones mat with two labeled columns, Tens and Ones. Prepare descriptions for five ten-strips, each representing ten equal units, and forty single-unit markers. The teacher supplies or prepares the actual accessible materials; this article specifies them rather than providing a completed printable file.
Keep the learner task and teacher key separate:
| Purpose | Learner-facing task | Teacher reference |
|---|---|---|
| Starting illustration | Explain the fictional written response 312 to 27 + 15 | Incorrect answer; its cause is not established |
| Worked example | Represent 27 and 15; combine and exchange | 3 tens + 12 ones = 4 tens + 2 ones = 42 |
| Contrast | Represent 23 + 14 | 3 tens + 7 ones = 37; no exchange needed |
| Independent check | Represent 28 + 16; write and explain the sum | 3 tens + 14 ones = 4 tens + 4 ones = 44 |
Leave the independent learner answer and explanation blank in the clean copy. A teacher key showing 44 is not evidence that a learner supplied it.
Model an exchange that preserves quantity
Place 2 ten-strips and 7 ones for 27, then 1 ten-strip and 5 ones for 15. Combining them gives 3 tens and 12 ones, worth 30 + 12 = 42.
Exchange ten of the twelve single units for one ten-strip. Remove those ten ones as the strip is added; keeping both would double-count their value. The result is 4 tens and 2 ones, still worth 40 + 2 = 42. The arrangement changes, but the total does not.
Connect the representation to written addition: twelve ones are represented by two in the ones place and one additional ten joined to the three tens. The final tens digit is four. The intermediate phrase “3 tens and 12 ones” describes a quantity; concatenating 3 and 12 into 312 does not write that quantity correctly.
Ask what the digits in the fictional response mean. Do not assume its writer concatenated counts unless the supplied explanation establishes that. The illustration gives a possible point to investigate, not a conclusion about an actual learner's thinking.
Use a proposed 20-minute sequence
- Inspect the starting response, 3 minutes: Ask for digit meanings and a representation. Record actual explanations only when provided.
- Model objects and notation, 5 minutes: Demonstrate 27 + 15 and the quantity-preserving exchange.
- Solve together and contrast, 5 minutes: Revisit the exchange, then compare 23 + 14. Seven ones need no exchange; do not perform one merely because the previous example did.
- Independent check, 4 minutes: Offer 28 + 16 with blank representation, answer and explanation fields. Keep the key out of this learner copy.
- Evidence and next step, 3 minutes: Note the observed representation, written notation, support used and unanswered question.
The phases total 3 + 5 + 5 + 4 + 3 = 20 minutes. These are planning allocations, not a speed contest or measured pupil performance.
The WWC's March 2021 practice-guide recommendations include systematic instruction, precise mathematical language and concrete or semi-concrete representations. This original place-value session uses those structural ideas. It is not a tested intervention protocol or a claim that one session produces mastery.
Let the independent evidence guide the next question
For the teacher, 28 + 16 combines to 3 tens and 14 ones, then exchanges to 4 tens and 4 ones, giving 44. The actual learner response remains unknown until observed.
Record the task ID, actual answer, representation, explanation, cue or support supplied, and proposed next step. If a response is unclear, ask the learner to represent the quantity or explain a digit. A correct numeral alone does not show how it was obtained; an incorrect numeral alone does not establish a diagnosis or intervention tier.
Retain the printable materials and required school observation record as the maintained originals. The companion compares before/after exchange and reveals a separate teacher key; resetting that display must not claim to erase school records or score a learner.
Copy a place-value reteaching brief
Create one complete, self-contained US-English HTML companion for “Math intervention • tens and ones”. Return the full HTML document, with inline CSS and any JavaScript needed for the local interactions. Use the original scenario, named records, numbers and expected cases below.
Design the page for this task: use clearly labeled input or source records, a readable result or worked example, and an adjacent explanation of the evidence. Use a restrained visual hierarchy, left-aligned text, readable tables or stacked records, and a responsive layout at 720px and 360px. Provide meaningful labeled controls for Model 27 + 15; Combine the quantities; Exchange 10 ones; Contrast 23 + 14; Review evidence completeness; Restore original timing; Select text; Select learner text. Use keyboard-accessible native controls and visible focus. Keep the complete content readable without an external dependency.
The following brief supplies the substantive content and constraints. Native-format requests describe the material to represent or copy manually; this HTML must not pretend to create DOCX, XLSX, PDF, PPTX, H5P or another native file, run Python/Flask/Django/Snowflake/Power BI, connect a live service, send messages, or perform an authorized real-world action. Where the task requires a native source, actual observation or separate approval, retain that requirement and leave unsupplied evidence blank.
Draft a math intervention lesson plan in US English.
Class/access context, teacher-supplied materials and duration: [enter]
Target mathematical idea: [enter]
Starting response and its provenance, fictional or actual sanitized: [paste]
Actual explanation/evidence: [paste or NOT YET OBSERVED]
Worked example, no-exchange contrast and independent task: [enter]
Required print format and school observation record: [enter]
Ask about digit meanings before inferring the cause of an error. Connect
objects, precise tens/ones language and notation. When exchanging ten ones
for one ten, preserve total quantity and remove the exchanged ones. Check all arithmetic. Keep independent learner fields blank and separate
from teacher keys. Make phase times sum to the duration. Record actual
representation, answer, explanation, support and unconfirmed next step. Do not invent pupil responses, diagnose from one error, assign a tier,
claim mastery or promise an intervention effect.
Return the proposed teacher sequence, clean learner material specification,
separate keys and blank evidence record in the required format. If requested,
specify an HTML teacher-review copy with local representation/step views. No automatic assessment, saved student scores or compulsory timed competition.
COMPLETE AUTHORED SCENARIO AND EXPECTED CASES
The following is the supplied reading/teaching/calculation record to represent in the companion. Preserve its particular content, examples, source references and unknowns. Wording about a future native implementation refers to that native task, not permission to omit this HTML companion.
# Math Intervention Lesson Plan Template: Connect the Exchange to the Written Digits
For 27 + 15, a starting response says “312.” Correcting it to 42 leaves an unanswered question: what does the learner think each digit represents? Ask for that explanation before deciding which support to use.
The response below is a fictional illustration, not an actual pupil record or a diagnosis. A short reteaching plan can connect objects, tens-and-ones language and written notation, then collect a separate independent response without inventing what the learner understood.
## Prepare the original representation task
Use a clean tens/ones mat with two labeled columns, **Tens** and **Ones**. Prepare descriptions for five ten-strips, each representing ten equal units, and forty single-unit markers. The teacher supplies or prepares the actual accessible materials; this article specifies them rather than providing a completed printable file.
Keep the learner task and teacher key separate:
| Purpose | Learner-facing task | Teacher reference |
| --- | --- | --- |
| Starting illustration | Explain the fictional written response 312 to 27 + 15 | Incorrect answer; its cause is not established |
| Worked example | Represent 27 and 15; combine and exchange | 3 tens + 12 ones = 4 tens + 2 ones = 42 |
| Contrast | Represent 23 + 14 | 3 tens + 7 ones = 37; no exchange needed |
| Independent check | Represent 28 + 16; write and explain the sum | 3 tens + 14 ones = 4 tens + 4 ones = 44 |
Leave the independent learner answer and explanation blank in the clean copy. A teacher key showing 44 is not evidence that a learner supplied it.
## Model an exchange that preserves quantity
Place **2 ten-strips and 7 ones** for 27, then **1 ten-strip and 5 ones** for 15. Combining them gives **3 tens and 12 ones**, worth **30 + 12 = 42**.
Exchange ten of the twelve single units for one ten-strip. Remove those ten ones as the strip is added; keeping both would double-count their value. The result is **4 tens and 2 ones**, still worth **40 + 2 = 42**. The arrangement changes, but the total does not.
Connect the representation to written addition: twelve ones are represented by two in the ones place and one additional ten joined to the three tens. The final tens digit is four. The intermediate phrase “3 tens and 12 ones” describes a quantity; concatenating 3 and 12 into 312 does not write that quantity correctly.
Ask what the digits in the fictional response mean. Do not assume its writer concatenated counts unless the supplied explanation establishes that. The illustration gives a possible point to investigate, not a conclusion about an actual learner's thinking.
## Use a proposed 20-minute sequence
1. **Inspect the starting response, 3 minutes:** Ask for digit meanings and a representation. Record actual explanations only when provided.
2. **Model objects and notation, 5 minutes:** Demonstrate 27 + 15 and the quantity-preserving exchange.
3. **Solve together and contrast, 5 minutes:** Revisit the exchange, then compare 23 + 14. Seven ones need no exchange; do not perform one merely because the previous example did.
4. **Independent check, 4 minutes:** Offer 28 + 16 with blank representation, answer and explanation fields. Keep the key out of this learner copy.
5. **Evidence and next step, 3 minutes:** Note the observed representation, written notation, support used and unanswered question.
The phases total **3 + 5 + 5 + 4 + 3 = 20 minutes**. These are planning allocations, not a speed contest or measured pupil performance.
The [WWC's March 2021 practice-guide recommendations](https://ies.ed.gov/ncee/wwc/practiceguide/26) include systematic instruction, precise mathematical language and concrete or semi-concrete representations. This original place-value session uses those structural ideas. It is not a tested intervention protocol or a claim that one session produces mastery.
## Let the independent evidence guide the next question
For the teacher, 28 + 16 combines to **3 tens and 14 ones**, then exchanges to **4 tens and 4 ones**, giving **44**. The actual learner response remains unknown until observed.
Record the task ID, actual answer, representation, explanation, cue or support supplied, and proposed next step. If a response is unclear, ask the learner to represent the quantity or explain a digit. A correct numeral alone does not show how it was obtained; an incorrect numeral alone does not establish a diagnosis or intervention tier.
Retain the printable materials and required school observation record as the maintained originals. The companion compares before/after exchange and reveals a separate teacher key; resetting that display must not claim to erase school records or score a learner.
## Copy a place-value reteaching brief
Implement the local companion rather than returning a text-only plan. Preserve every numerical fixture and the distinction between illustrative expectations and actual evidence. Any native-runtime or classroom tests mentioned above remain tests to perform in the proper environment; do not mark them passed. Keep edits and practice responses in this open page only, without claiming persistent storage. Provide invalid/missing-input feedback and reset behavior that agree with this specific brief. Do not claim accessibility certification, learning gains, real approvals or test results that were not observed.
Have a teaching colleague check that the exchange changes the arrangement while preserving 42, then inspect the blank independent task beside its separate key. Keep actual observations in the required school record, and choose the next support from what the learner represents and explains rather than from the fictional starting answer.