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This is the October 2023 edition of the Transum Newsletter. The month that begins with 'oct' just like octagon, octahedron, octuplets, octet, octogenarian and octopus yet, due to the development of the calendar, means the 10th month not the 8th.

Without further ado here is the puzzle of the month:

Find two whole numbers that, when multiplied, give you a whopping 1,000,000! But here's the twist: neither number can have a zero as one or more of it's digits.

While you think about that here are some of the key resources added to the Transum website during the last month.

Pattern Clues has been reimagined! It has been rewritten so that it is now self-checking. Pupils will need a very basic knowledge of ratio to make use of some of the clues. The activity is based on a SMP11-16 groupwork task intended for groups of four or five pupils. While I think the group situation is the best setting, this version accommodates pupils working alone without another three or four pupils to make up a group.

Thanks to Transum friend Ann who suggested an additional level to the Quadratic Sequences exercise in which pupils have to find the missing terms. The commonly used strategy of applying the difference method (as shown in the help tab) won't work directly as the missing terms break up the runs of three or more consecutive terms given. The answer section for subscribers show some working and thoughts. Thanks Ann.

I have added a new level to the Advanced Trigonometry Exercises which contains a mixture of sine rule, cosine rule, and sine formula for the area of a triangle questions. Don't tell your students. But I actually used the versatile Triangle Solver to work out all the answers instead of plodding through the formulas with a calculator!

The Starter of The Day main page has been changed. The calendar in now much bigger and the title of the Starter now appears as a 'tool tip' as your mouse hovers over each date.

Following last month's pirate themed number chanting, this month I have redesigned the Numbers in Words - Words in Digits activity. The ability for children to read and write numbers as words is a fundamental skill that fosters a deeper understanding of mathematics and its practical applications while appreciating the irregularities of our natural numbers.

Continuing my experiments using artificial intelligence (AI) I would like to present the following mash up of key takeaways from three great names in the world of education.Combining the insights from Professor John Hattie, Barak Rosenshine, and Peps McCrea, here are the top five most important strategies/methods/techniques for maths teachers:

1. Clear Learning Goals and Objectives:

- Set explicit, transparent, and specific objectives for what students should achieve. This provides direction for both teaching and learning. [Example: The purpose of Transum online exercises appear below the title]

2. Structured Instruction and Scaffolding:

- Break down complex problems into manageable steps, guiding students through each one. Provide temporary support (scaffolding) as students learn new skills, gradually reducing that support as they become proficient. [Example: Most Transum online exercise are presented in levels to provide the scaffolding in the early stages]

3. Regular Feedback and Formative Assessments:

- Engage students with timely and specific feedback to help them recognize their next steps. Use formative assessments to continuously evaluate and adapt to students' understanding, addressing misconceptions early. [Example: Students are encouraged to press the Check button often as they work through an exercise rather than leaving it till the end.]

4. Active Questioning and Independent Practice:

- Regularly challenge students with questions to assess their understanding. After guided practice, ensure students have the opportunity to apply concepts independently, solidifying their grasp of the material. [Examples: The puzzles, games, investigations and Starters found on the Transum website.]

5. Regular Review and Metacognitive Strategies:

- Reinforce previous learning through weekly and monthly reviews. Encourage students to reflect on their thinking processes, fostering self-regulated learning and deeper understanding. Examples: Refreshing Revision and Revision resources.]

By focusing on these five key strategies, mathematics teachers can enhance their teaching effectiveness and support students in mastering mathematical concepts more efficiently.

If you are a Transum Subscriber and use Class Admin to automatically keep track of the trophies your pupils have earned you may be pleased that there is now a chronological list of trophies earned for each pupil in your class available. Thanks Paul for the suggestion.

The month of October ends with Halloween. The Starter of the Day for the 31st has spooky music and screams to make the day memorable while solving ghostly maths problems. There’s only one thing I don’t like about Halloween… which is …

For future reference there is a 'mirror' site that contains all the Transum Starters and activities. It is at www.transum.info The only difference is that it doesn't contain the details of your Transum subscription account so you won’t be able to log in there. If it happens that for some reason Transum.org goes offline you can use the mirror site until the main site is restored.

Finally the answer to last month's puzzle which was: "A dartboard breaks into two pieces. The sum of the numbers on one piece is twice the sum of the numbers on the other piece. Where was the break?"

The break line started between the 18 and 4 and ended between the 19 and 3 thus the sum of the numbers on one piece {4, 13, 6, 10, 15, 2, 17, 3} is 70.

Given that the total sum of all numbers on the dartboard is 210, the sum of the numbers on the other piece would be 210 - 70 = 140.

Since 140 is twice 70, this solution is correct.

I used a spreadsheet to find the answer but I think Chris Smith did all of the calculations in his head. Respect!

That's all for now,

John

P.S. Why did the pupil learning number bases think that Halloween was the same as Christmas?

Because 31 _{OCT} = 25 _{DEC}.

Do you have any comments? It is always useful to receive feedback on this newsletter and the resources on this website so that they can be made even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.