Chapter 13, Strategies for Whole-Number Computation Video Solutions, Elementary and Middle School Mathematics: Teaching Developmentally, 6th edition

Problem 1

What is the difference between solving a problem with direct modeling and solving a problem with an invented strategy? What is a traditional algorithm?

Ankit Gupta

Numerade Educator

04:23

Problem 2

How are traditional algorithms different from invented strategies? Explain the benefits of invented strategies over traditional algorithms.

Nicholas Mogoi

Numerade Educator

01:30

Problem 3

When a problem has been solved, how do you manage all of the different methods that students may propose, and what should you do about students who propose no ideas of their own?

Emily Himsel

Numerade Educator

01:12

What do you do when someone brings a traditional algorithm into the classroom before you have introduced it? What if you never plan to teach the traditional algorithm but students want to use it anyway?

Ashley High

Numerade Educator

01:49

Problem 5

Explain how strategies for problems sach as $58+6$ or $72-$ 5 are similar to the make-ten strategies for basic facts. How can you help children extend their basic fact strategies to these larger numbers?

Suman Saurav Thakur

Numerade Educator

11:00

Problem 6

Illustrate three different strategies for adding $46+39$, Which ones are easy to do mentally? Is there a strategy that is easier because 39 is close to 40 ? What strategies work well for sums such as $538+243$ ? For each strategy you work with, think about how you could record it on the board so that other students will be able to follow what is being done.

Chris Trentman

Numerade Educator

02:01

Problem 7

Use two different adding-up strategies for $93-27$ and for $545-267$. Make up a story problem that would encourage an adding-up strategy.

Suman Saurav Thakur

Numerade Educator

02:10

Problem 8

Describe how you would go about developing the traditional algorithms for addition and subtraction. How would you deal with the issue of beginning on the right with the ones place when students' natural tendency is to begin on the left? Use $385+128$ to illustrate a reasonable written algorithm that begins on the left instead of the right. Do the same for 453 - 278 .

Adriano Chikande

Numerade Educator

01:58

Problem 9

Draw pictures showing how $57 \times 4$ could be modeled: with counters, with base-ten pieces, with rectangles or arrays on base-ten grids.

Anna Jones

Numerade Educator

01:30

Problem 10

What would you do if your students seemed to persist in using complete-number strategies for multiplication (variations of repeated addition without really doing any multiplication)?

Emily Himsel

Numerade Educator

01:11

Problem 11

What is a cluster problem? Make up cluster problems for $46 \times 5$ and $73 \times 18$

Kayla Laughman

Numerade Educator

00:44

Problem 12

Try to develop some skill using an invented strategy for multiplying by single-digit numbers. Can you do $327 \times 6$ mentally? How would you record the steps on the chalkboard if a student gave them to you the way you did it?

Julie Silva

Numerade Educator

00:25

Problem 13

Use a compensation strategy for these: $68 \times 20,5 \times 46,25$ $\times 480$.

Michelle Nguyen

Numerade Educator

01:40

Problem 14

Draw a rectangle for $28 \times 57$, and explain how it could be used to compute the product.

Cory Kuzinski

Numerade Educator

View

Problem 15

Which division concept, measurement or partition, is easier for direct modeling and is also the one used to develop the usual long-division algorithm? Make up an appropriate word story with that concept to go with $735 \div 6$.

Lauren Long

Numerade Educator

01:10

Problem 16

Explain a missing-factor strategy for division. Use that approach to solve $264 \div 12$. Repeat the problem using a different starting point.

Kayla Laughman

Numerade Educator

01:42

Problem 17

Use the traditional algorithm for $735+6$, and then repeat the process using the text's suggestion of recording trades explicitly. With the two algorithms side by side, explain every recorded number in terms of what it stands for when sharing base-ten pieces.

James Chok

Numerade Educator

02:19

Problem 18

To avoid erasures in long division, a rounded-up divisor can be used to make estimates of the quotient in each place value. Show how this method works and avoids erasures using the problem $4589+62$