A three-lesson teacher plan connecting place-value multiplication, division decisions and repeating cycles through equal groups. Reuse three existing 40-minute investigations with parallel entry and exit evidence.
Anonymous group code: __________ Date: __________
Before the sequence
Work independently. Write a number with its unit, and record the explanation requested. Your teacher will record the answer and the reasoning separately.
pre1. For 132 × 24, a draft correctly finds 132 × 4 = 528 but writes 264 as the row for 132 × 20. Enter the corrected value of that second row and explain what the 2 in 24 represents.
pre2. Each of 23 packs contains 148 labels. Enter the total number of labels. Write the partial products for twenty packs and three packs and explain why they are added.
pre3. There are 83 indivisible cards. Each issued kit must contain exactly six cards; incomplete kits are not issued and spare cards remain in storage. Enter the number of complete kits. Write a quotient-and-remainder equation and state what happens to the spare cards.
pre4. All 94 indivisible cards must travel in envelopes holding at most seven cards each. A partly filled final envelope is allowed. Enter the minimum envelope count, show why one fewer cannot carry every card and why your count can.
pre5. Two carts are together at a doorway at 10:00 a.m. and return every four and eight minutes from that same start. Enter the elapsed minutes until their next meeting after 10:00. List enough returns to show it is the first later meeting.
pre6. Two carts are together at 2:00 p.m. and return every three and five minutes from that same start. How many meetings occur after 2:00 and up to 2:45, including the endpoint? Enter the count and list their meeting times. Show each cart's returns through the first later meeting.
After the sequence
Use this set after the lessons. Work without a partner first. Explain your method; a correct number alone does not show every part of your reasoning.
post1. For 214 × 32, a draft correctly finds 214 × 2 = 428 but writes 642 as the row for 214 × 30. Enter the corrected value of that second row and explain what the 3 in 32 represents.
post2. Each of 34 packs contains 126 labels. Enter the total number of labels. Write the partial products for thirty packs and four packs and explain why they are added.
post3. There are 97 indivisible cards. Each issued kit must contain exactly eight cards; incomplete kits are not issued and spare cards remain in storage. Enter the number of complete kits. Write a quotient-and-remainder equation and state what happens to the spare cards.
post4. All 119 indivisible cards must travel in envelopes holding at most eight cards each. A partly filled final envelope is allowed. Enter the minimum envelope count, show why one fewer cannot carry every card and why your count can.
post5. Two carts are together at a doorway at 11:00 a.m. and return every three and nine minutes from that same start. Enter the elapsed minutes until their next meeting after 11:00. List enough returns to show it is the first later meeting.
post6. Two carts are together at 9:00 a.m. and return every three and eight minutes from that same start. How many meetings occur after 9:00 and up to 9:48, including the endpoint? Enter the count and list their meeting times. Show each cart's returns through the first later meeting.
Transfer the reasoning
transfer. An office opens 24 packs containing 36 cards each. All cards must travel in envelopes holding at most seven indivisible cards; a partly filled last envelope is allowed. Two carts are together at the office at 9:10 a.m. and return every four and nine minutes from that common start. The office will hand over the batch at their first meeting after the start. Write a decision note giving the total cards, minimum envelopes, cards in the last envelope, elapsed wait and handover clock time. Show a group-value calculation, an insufficient/sufficient capacity check and return-list evidence.