Scope & Sequence Question for Mathematics: An Instrument for Living Teaching

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• Mamatoto
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I could use some help defining some of the terms in the 4th grade arithmetic scope and sequence.  We have progressed through most of the topics this year, but I have a few left unchecked simply because I don’t know if I understand the meaning of topic correctly:

• Under subtraction: “sums using brackets” – is this the concept of solving problems inside parentheses first?  If so, it seems a funny place to put the topic because a string of numbers being added or subtracted can be done in any order.  It only makes a difference when mixing addition/subtraction with multiplication/division.
• Under subtraction: “harder compound addition using money” and “harder compound subtraction using money” -what does “compound” refer to?
• Under multiplication: “short compound multiplication using money” – again, what does “compound” refer to?  I can only think of the term “compound interest” but am guessing that isn’t what is being referred to for a 4th grader.
• Under multiplication: “multiplication by a product” – Is this a problem where the child would need to solve several problems in steps to get the final answer, using the answer of the first step as multiplicand of the second step?
• Under multiplication: “rules to help get multiplication sums right” – any ideas on what some of the rules might be?
• Under division: “division of one quantity by another” – how is this different from just plain “division?”
• Under division: “rules to help get division sums right” – again, any ideas?

Thanks in advance for any insight!!

Richele Baburina
Participant

Hi mamatoto,

Would you mind waiting for a complete answer from me on this? I’m currently traveling overseas without my computer.

I don’t see anything on the list that would keep one from finishing out the school year, though, if you’re waiting on it.

Best,

Richele

Mamatoto
Participant

I can absolutely wait!  Thank you and happy travels!!!

Richele Baburina
Participant

Hi Mamatoto and thanks for your patience. Let me start right off the bat by saying that Miss Mason’s scope & sequences weren’t static so, if you are using a simple math book along with her methods of teaching arithmetic, you might go ahead and use that book’s sequence if it’s a nicely graduated one. Here we go:

“sums using brackets” – You’re correct, the idea here is that in problems of this type it can be done both ways.

“harder compound addition using money” and “harder compound subtraction using money” -what does “compound” refer to? – The term “compound” here is the standard dictionary definition of something composed of two or more separate elements. In our case, it might be pennies, dimes, and dollars.

Under multiplication: “short compound multiplication using money” – again, what does “compound” refer to?  – Right, this is again something like multiplying 1 dollar and 37 cents by 7. 7 cents x 7 is 4 dimes and 9 cents. As you continue to multiply, you exchange the money (pennies to dimes, dimes to dollars, etc.)

Under multiplication: “multiplication by a product” – This is kind of a cool thing for multiplying mentally or it may just be more expedient: We know when two (or more) numbers are multiplied together, the answer is called the “product”. 8 is the product of 2 x 4, 25 is the product of 5 x 5.  35 is the product of 5 x 7 (what we commonly call factors) Rather than taking the time to multiply 284 by 35, we could first multiply it by 5 and then multiply the result by 7 to achieve the same answer as if we multiplied it by 35. You can try a few of these both ways and see which you work more quickly.

“rules to help get multiplication sums right” and “rules to help get division sums right”, any ideas?– The simplest I can think of is taking the answer and dividing it by either the multiplier or multiplicand for multiplication and for division, taking the answer and multiplying it by the divisor to see if you get the dividend.

“division of one quantity by another” – how is this different from just plain “division?”- This is much like that term “compound” above.  For example, if you are dividing a feet by inches, you’d turn the feet to inches first. In a pacing exercise, you might know your pace is 30″ so how would you find out how many steps you must take to travel 100 feet?

I hope this is a help to you.
Best,
Richele

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