Question 1

Show 3335 ÷ 23 with a scaffolding algorithm and then by the standard algorithm. Show how each number in the standard algorithm is associated with each number in the scaffolding algorithm.

Accepted Answer

In the second algorithm, the 23 actually is 2300, yielding 100 in the quotient. The 103 is actually 1030, from which 920 (i.e., 23 × 40, which is 460 twice, making the first division easier) is subtracted, leaving 115 in both algorithms. In the first algorithm, 115 ÷ 23 is done in two steps, and in one step in the second algorithm, both times yielding 5. The first scaffolding algorithm could be done in multiple ways yielding the same result.

Question 2

Use the scaffolding method to compute 5883 ÷ 17.

Accepted Answer

Something along the lines of the following, which unnecessarily gives the best guesses for each place value (one of the talking points for the scaffolding algorithm):

Question 3

Show, using 324 ÷ 28, how to work from the scaffolding algorithm to the standard algorithm.

Accepted Answer

Similar to question 1. Students' work should show an awareness of the scaffolding algorithm format to an abbreviated form to the usual US form.

Question 4

Do 32 × 467 using the method of writing all partial products.

Accepted Answer

The answer of Do 32 × 467 using the method...

Question 5

Use a nonstandard algorithm to find 240_five + 314_five, but showing all partial sums.

Accepted Answer

The answer of Use a nonstandard algorithm to find 240_five...

Question 6

Name two positive and two negative aspects of learning nonstandard algorithms.

Accepted Answer

The answer of Name two positive and two negative aspects...

Question 7

Make a drawing of base-ten materials that shows the initial setup for 3 × 130.2. Make clear what = 1. Do not take time to draw all the later steps of the calculation with the base ten materials.

Accepted Answer

The answer of Make a drawing of base-ten materials that...

Question 8

Draw how one would act out 200 - 62 (take-away view) to support the usual right-left algorithm, with base-ten materials. (Make clear what represents 1.) Make a separate drawing for each step (add steps if you need them).

Accepted Answer

The answer of Draw how one would act out 200...

Question 9

Draw how one would act out 200 - 62 (comparison view) to support the usual right-left algorithm, with base-ten materials. (Make clear what represents 1.) Make a separate drawing for each step (add steps if you need them).

Accepted Answer

The answer of Draw how one would act out 200...

Question 10

You decide to introduce your fourth-graders to the long-division algorithm with one-digit divisors, using base-ten materials and 96 ÷ 3. You also want to use a story problem that they would find interesting as the basis for their work.
A) From the practical standpoint of acting out the calculation, which way of thinking about division-repeated subtraction or sharing equally-should you use in your story problem for 96 ÷ 3?
B) Write such a story problem (involving 96 ÷ 3).
C) Show how you would act out your story problem, with drawings of the base-ten materials.
D) Write a second story problem for 96 ÷ 3, involving a different way of thinking about division from the way of thinking in your story problem in part
E) Answer parts A-D if you were to use 960 ÷ 320 instead of 96 ÷ 3.

Accepted Answer

The answer of You decide to introduce your fourth-graders to...

Question 11

A student places multi-base blocks on the table as follows:  
Write which calculation the student might be doing. A. $ 226 + 49$
B. $226 - 49$
C. $226 - 134$
D. $226 - 118$

Accepted Answer

The answer of A student places multi-base blocks on the...

Question 12

What would the NEXT line be in a Russian peasant calculation of 23 × 621?
You do not have to do the complete algorithm.
23 × 621
A) 11 × 1242
B) 46 × 310
C) 23 × 21
D) 11 × 1242 or possibly 46 × 310
E) 46 × 310 or possibly 23 × 21

Accepted Answer

The Russian peasant multiplication algorithm involves halving one number and doubling the other, discarding any fractions that result from the halving. Both 11 × 1242 (halving 23 and doubling 621) and 46 × 310 (doubling 23 and halving 621) are valid next steps depending on whether you choose to halve the first number and double the second, or vice versa.

Question 13

The Russian peasant method for multiplying uses two basic processes: doubling and _____.

Accepted Answer

The answer of The Russian peasant method for multiplying uses...

Question 14

Below is a worked-out calculation of 313 × 42, using the lattice method for multiplication. Explain why the method does give the correct number in the tens place (the circled 4). (Note: Some current textbooks use this algorithm to teach multiplication of whole numbers.)

Accepted Answer

The answer of Below is a worked-out calculation of 313...

Question 15

Write a word problem that would require solving 540 ÷ 4.

Accepted Answer

The answer of Write a word problem that would require...

Question 16

Consider this arithmetic problem:

A) Write a story problem where the answer would be 6.
B) Write a story problem where the answer would be 7.
C) Write a story problem where the answer would be 1.
D) Write a story problem where the answer would be 6$1 / 4$

Accepted Answer

The answer of Consider this arithmetic problem:

A) Write...

Question 17

A student's work on a base-ten subtraction problem is shown below. How much does the little 1 above the 5 represent?

Accepted Answer

The answer of A student's work on a base-ten subtraction...

Quiz 4: Some Conventional Ways of Computing

Show 3335 ÷ 23 with a scaffolding algorithm and then by the standard algorithm. Show how each number in the standard algorithm is associated with each number in the scaffolding algorithm.

Use the scaffolding method to compute 5883 ÷ 17.

Show, using 324 ÷ 28, how to work from the scaffolding algorithm to the standard algorithm.

Do 32 × 467 using the method of writing all partial products.

Use a nonstandard algorithm to find 240_five + 314_five, but showing all partial sums.

Name two positive and two negative aspects of learning nonstandard algorithms.

Make a drawing of base-ten materials that shows the initial setup for 3 × 130.2. Make clear what = 1. Do not take time to draw all the later steps of the calculation with the base ten materials.

Draw how one would act out 200 - 62 (take-away view) to support the usual right-left algorithm, with base-ten materials. (Make clear what represents 1.) Make a separate drawing for each step (add steps if you need them).

Draw how one would act out 200 - 62 (comparison view) to support the usual right-left algorithm, with base-ten materials. (Make clear what represents 1.) Make a separate drawing for each step (add steps if you need them).

A student places multi-base blocks on the table as follows: Write which calculation the student might be doing. A. $226 + 49$ B. $226 - 49$ C. $226 - 134$ D. $226 - 118$

What would the NEXT line be in a Russian peasant calculation of 23 × 621? You do not have to do the complete algorithm. 23 × 621

The Russian peasant method for multiplying uses two basic processes: doubling and _____.

Below is a worked-out calculation of 313 × 42, using the lattice method for multiplication. Explain why the method does give the correct number in the tens place (the circled 4). (Note: Some current textbooks use this algorithm to teach multiplication of whole numbers.)

Write a word problem that would require solving 540 ÷ 4.

Consider this arithmetic problem: A) Write a story problem where the answer would be 6. B) Write a story problem where the answer would be 7. C) Write a story problem where the answer would be 1. D) Write a story problem where the answer would be 6 $1 / 4$

A student's work on a base-ten subtraction problem is shown below. How much does the little 1 above the 5 represent?

Quiz 4: Some Conventional Ways of Computing

Show 3335 ÷ 23 with a scaffolding algorithm and then by the standard algorithm. Show how each number in the standard algorithm is associated with each number in the scaffolding algorithm.

Use the scaffolding method to compute 5883 ÷ 17.

Show, using 324 ÷ 28, how to work from the scaffolding algorithm to the standard algorithm.

Do 32 × 467 using the method of writing all partial products.

Use a nonstandard algorithm to find 240five + 314five, but showing all partial sums.

Name two positive and two negative aspects of learning nonstandard algorithms.

Make a drawing of base-ten materials that shows the initial setup for 3 × 130.2. Make clear what = 1. Do not take time to draw all the later steps of the calculation with the base ten materials.

Draw how one would act out 200 - 62 (take-away view) to support the usual right-left algorithm, with base-ten materials. (Make clear what represents 1.) Make a separate drawing for each step (add steps if you need them).

Draw how one would act out 200 - 62 (comparison view) to support the usual right-left algorithm, with base-ten materials. (Make clear what represents 1.) Make a separate drawing for each step (add steps if you need them).

A student places multi-base blocks on the table as follows: Write which calculation the student might be doing. A. 226+49 226 + 49226+49 B. 226−49226 - 49226−49 C. 226−134226 - 134226−134 D. 226−118226 - 118226−118

What would the NEXT line be in a Russian peasant calculation of 23 × 621? You do not have to do the complete algorithm. 23 × 621

The Russian peasant method for multiplying uses two basic processes: doubling and _____.

Below is a worked-out calculation of 313 × 42, using the lattice method for multiplication. Explain why the method does give the correct number in the tens place (the circled 4). (Note: Some current textbooks use this algorithm to teach multiplication of whole numbers.)

Write a word problem that would require solving 540 ÷ 4.

Consider this arithmetic problem: A) Write a story problem where the answer would be 6. B) Write a story problem where the answer would be 7. C) Write a story problem where the answer would be 1. D) Write a story problem where the answer would be 6 1/41 / 41/4

A student's work on a base-ten subtraction problem is shown below. How much does the little 1 above the 5 represent?

Use a nonstandard algorithm to find 240_five + 314_five, but showing all partial sums.

A student places multi-base blocks on the table as follows: Write which calculation the student might be doing. A. $226 + 49$ B. $226 - 49$ C. $226 - 134$ D. $226 - 118$

Consider this arithmetic problem: A) Write a story problem where the answer would be 6. B) Write a story problem where the answer would be 7. C) Write a story problem where the answer would be 1. D) Write a story problem where the answer would be 6 $1 / 4$