# Put quantities on a line Current generated source edition; original unpiloted timing and teaching limits remain. ## Day 67 ## Title Put quantities on a line ## Focus Neighbouring quantities and a declared 1000 boundary ## Codes - AC9M2N01 ## Purpose Make a clear quantity guide that preserves stated values and helps someone compare or arrange fictional label quantities. ## Entry Check actual three-digit place-value opportunities from earlier lessons; do not assume Days 51–60 teach this. If a hundred/tens/ones model is unclear, explicitly teach 100=10 tens,10=10 ones with a smaller example first. ## Materials Large paper/pen, optional safe large markers or tactile labels. No purchase, robot, screen, outing, real money or private location disclosure is required. Choose one route, not all three. ## Complete ordinary source Fictional quantity card set: Label counts around four hundred. First card states 390 labels; second card states 400 labels; third card states 410 labels. These are stated counts of the same kind of label, not observed stocks, money, distances or prices. An extra number-line guide states 390,400,410,420 in this order, with equal ten-label intervals. The task is to represent, compare or order these stated quantities and give a checking reason. ## First invitation Make a useful quantity guide. Keep the whole quantity and the value of each digit clear. ## Full teacher model 390 = 3 hundreds + 9 tens + 0 ones = 300 + 90 + 0. 400 = 4 hundreds + 0 tens + 0 ones = 400 + 0 + 0. 410 = 4 hundreds + 1 ten + 0 ones = 400 + 10 + 0. Ascending order is 390, 400, 410. Compare the first differing place from the highest place, rather than the last digit alone. Use a number-line guide with four equally spaced ticks labelled 390, 400, 410, 420 from left to right. The four ticks bound three equal ten-label intervals. Place the 390 card at the first tick, 400 at the second and 410 at the third; 420 is the final supplied scale label, not a fourth quantity card. One interval right adds ten labels and one interval left removes ten. The positions and equal intervals explain the same ordering; counting the tick labels is not counting the intervals. ## Guided source Fictional quantity card set: New line-label counts. First card states 890 labels; second card states 900 labels; third card states 910 labels. These are stated counts of the same kind of label, not observed stocks, money, distances or prices. Equal ten-label ticks 880,890,900,910 are supplied. Then separately compare 999 with 1000 using 10 hundreds. The task is to represent, compare or order these stated quantities and give a checking reason. ## Guided invitation Make a useful quantity guide. Keep the whole quantity and the value of each digit clear. ## Guided staff possibility 890 = 8 hundreds + 9 tens + 0 ones = 800 + 90 + 0. 900 = 9 hundreds + 0 tens + 0 ones = 900 + 0 + 0. 910 = 9 hundreds + 1 ten + 0 ones = 900 + 10 + 0. Ascending order is 890, 900, 910. Compare the first differing place from the highest place, rather than the last digit alone. Use the supplied four equally spaced ticks labelled 880, 890, 900, 910. They bound three equal ten-label intervals. The 890 card belongs at the second tick, 900 at the third and 910 at the fourth; 880 is a scale label. Moving one interval changes the count by ten labels. Count intervals separately from ticks. For the separate 999-to-1000 boundary, show 999 as 9 hundreds, 9 tens and 9 ones. Add 1 one: 9 hundreds, 9 tens and 10 ones. Manually exchange 10 ones for 1 ten: 9 hundreds, 10 tens and 0 ones. Manually exchange 10 tens for 1 hundred: 10 hundreds, 0 tens and 0 ones = 1000. Ten hundreds have the value of 1 thousand. The quantity increases only when the extra one is added; each exchange preserves the resulting whole. Use chosen 100/10/1 cards or paper bundles; no automatic exchange is required. ## Six moves #### Minutes 0–3 #### Action Name the useful job and receive a first own idea from the whole ordinary source. #### Minutes 3–9 #### Action On separate adult work, explicitly model the mathematical relationship using the complete source and after-own staff account. #### Minutes 9–15 #### Action Give the complete different guided source. Let the learner direct/describe before showing its staff possibility. Note mathematical hints. #### Minutes 15–22 #### Action Choose one full route and make a useful own guide; switching, rest or a shorter component is allowed. #### Minutes 22–25 #### Action Receive one fresh component from an eligible neutral family or a new changed full source before its staff model. #### Minutes 25–29 #### Action Keep one practical result and identify one specific next teaching opportunity from actual evidence. These timings are adjustable. ## Routes #### Id D67-R1 #### Title Label counts around four hundred #### Source Fictional quantity card set: Label counts around four hundred. First card states 390 labels; second card states 400 labels; third card states 410 labels. These are stated counts of the same kind of label, not observed stocks, money, distances or prices. An extra number-line guide states 390,400,410,420 in this order, with equal ten-label intervals. The task is to represent, compare or order these stated quantities and give a checking reason. #### Purpose Make a useful quantity guide. Keep the whole quantity and the value of each digit clear. #### Moves - Receive a first idea with no supplied solution. - Represent the stated quantities, then compare/order or rename exactly as the source requests. Explain what each place and result counts. - Try the idea on the same complete paper source; an agreeing helper moves or scribes exactly as directed. - Keep one useful guide and one checking sentence. A proposed reader test stays proposed. #### After own staff possibility 390 = 3 hundreds + 9 tens + 0 ones = 300 + 90 + 0. 400 = 4 hundreds + 0 tens + 0 ones = 400 + 0 + 0. 410 = 4 hundreds + 1 ten + 0 ones = 400 + 10 + 0. Ascending order is 390, 400, 410. Compare the first differing place from the highest place, rather than the last digit alone. Use a number-line guide with four equally spaced ticks labelled 390, 400, 410, 420 from left to right. The four ticks bound three equal ten-label intervals. Place the 390 card at the first tick, 400 at the second and 410 at the third; 420 is the final supplied scale label, not a fourth quantity card. One interval right adds ten labels and one interval left removes ten. The positions and equal intervals explain the same ordering; counting the tick labels is not counting the intervals. #### Different try Choose a different representation of the same given whole or a clearly stated new quantity. Recalculate/reorder instead of carrying an earlier answer. #### Optional access Speech, signing, AAC, pointing, marks, tactile row/column labels or exact dictation are available. Record any supplied mathematical choice separately; pause/skip/solo work is fine. #### Id D67-R2 #### Title Just before one thousand #### Source Fictional quantity card set: Just before one thousand. First card states 998 labels; second card states 999 labels; third card states 1000 labels. These are stated counts of the same kind of label, not observed stocks, money, distances or prices. Ten hundreds represent 1000. Its numeral has four digits; it is the taught boundary, not a three-digit quantity. The task is to represent, compare or order these stated quantities and give a checking reason. #### Purpose Make a useful quantity guide. Keep the whole quantity and the value of each digit clear. #### Moves - Receive a first idea with no supplied solution. - Represent the stated quantities, then compare/order or rename exactly as the source requests. Explain what each place and result counts. - Try the idea on the same complete paper source; an agreeing helper moves or scribes exactly as directed. - Keep one useful guide and one checking sentence. A proposed reader test stays proposed. #### After own staff possibility 998 = 9 hundreds + 9 tens + 8 ones = 900 + 90 + 8. 999 = 9 hundreds + 9 tens + 9 ones = 900 + 90 + 9. 1000 = 10 hundreds + 0 tens + 0 ones = 1000 + 0 + 0. Ascending order is 998, 999, 1000. Compare the first differing place from the highest place, rather than the last digit alone. On separate teacher paper, place 998, 999, 1000 in order at three equally spaced one-label ticks. There are two one-label intervals. The jump from 999 to 1000 crosses the named boundary, even though the final numeral has four digits. For the separate 999-to-1000 boundary, show 999 as 9 hundreds, 9 tens and 9 ones. Add 1 one: 9 hundreds, 9 tens and 10 ones. Manually exchange 10 ones for 1 ten: 9 hundreds, 10 tens and 0 ones. Manually exchange 10 tens for 1 hundred: 10 hundreds, 0 tens and 0 ones = 1000. Ten hundreds have the value of 1 thousand. The quantity increases only when the extra one is added; each exchange preserves the resulting whole. Use chosen 100/10/1 cards or paper bundles; no automatic exchange is required. #### Different try Choose a different representation of the same given whole or a clearly stated new quantity. Recalculate/reorder instead of carrying an earlier answer. #### Optional access Speech, signing, AAC, pointing, marks, tactile row/column labels or exact dictation are available. Record any supplied mathematical choice separately; pause/skip/solo work is fine. #### Id D67-R3 #### Title Counts around six hundred #### Source Fictional quantity card set: Counts around six hundred. First card states 590 labels; second card states 600 labels; third card states 610 labels. These are stated counts of the same kind of label, not observed stocks, money, distances or prices. The supplied number-line ticks 590,600,610,620 are equal ten-label intervals. The task is to represent, compare or order these stated quantities and give a checking reason. #### Purpose Make a useful quantity guide. Keep the whole quantity and the value of each digit clear. #### Moves - Receive a first idea with no supplied solution. - Represent the stated quantities, then compare/order or rename exactly as the source requests. Explain what each place and result counts. - Try the idea on the same complete paper source; an agreeing helper moves or scribes exactly as directed. - Keep one useful guide and one checking sentence. A proposed reader test stays proposed. #### After own staff possibility 590 = 5 hundreds + 9 tens + 0 ones = 500 + 90 + 0. 600 = 6 hundreds + 0 tens + 0 ones = 600 + 0 + 0. 610 = 6 hundreds + 1 ten + 0 ones = 600 + 10 + 0. Ascending order is 590, 600, 610. Compare the first differing place from the highest place, rather than the last digit alone. Use the supplied four equally spaced ticks labelled 590, 600, 610, 620. They bound three equal ten-label intervals. Place 590 at the first tick, 600 at the second and 610 at the third; 620 completes the scale. Moving one interval changes the count by ten labels, so positions and equal spacing support the comparison. #### Different try Choose a different representation of the same given whole or a clearly stated new quantity. Recalculate/reorder instead of carrying an earlier answer. #### Optional access Speech, signing, AAC, pointing, marks, tactile row/column labels or exact dictation are available. Record any supplied mathematical choice separately; pause/skip/solo work is fine. ## Misconception Ranks quantities from the last digit or counts included number-line labels instead of equal intervals. Name the full numerals and each supplied interval. ## Review Look for a correct whole representation, clear result units and valid ordering/renaming reason. A numeral copied from a model, fast answer or completed field count is not independent evidence. ## Held offer An eligible single neutral component may inform teaching; completing every held source is unnecessary. ## Next teaching Choose the exact matching component-specific complete NEXT after receiving the actual response. If the relationship is unavailable, teach it; leave unobserved components open. ## Own blank ### Job ### Source known ### Goal ### Model ### Method ### Result ### Check ## Status Dated original planning status (13 October2026): Original unpiloted WRITTEN plan; no administered assessment, implemented helper or live lesson claim.