Week 8 Assignment 4

Reasoning Strategy 1 – One more one less: In grades K-1, students learn the counting sequence, and practice counting on from a given number.  These skills provide a foundation for finding “one more” and “one less (e.g., 5+1 and 5-1).  The hundreds chart can be a useful tool for visualizing numbers relationships when working with these addition and subtraction facts.  It can also support students when they begin finding “ten more” and “ten less”.

NOTE:  Use this

interactive hundred chart

to answer questions 1-2.  

1.

On your hundred chart, mark each starting number in yellow. Then, mark each sum or difference in pink.

a. Starting number 3.  Add 1.

a. Starting number 6.  Subtract 1.

a. Starting number 8.  Add 1.

a. Starting number 10.  Subtract 1.

a. Starting number 25.  Add 1

a. Starting number 37.  Subtract 1.

Put a screenshot of your completed hundred chart here:

0. On your hundred chart, mark each starting number in yellow. Then, mark each sum or difference in pink.

a. Starting number 22.  Add 10.

b. Starting number 22.  Subtract 10.

c. Starting number 45.  Add 10.

d. Starting number 45.  Subtract 10.

e. Starting number 68.  Add 10.

f. Starting number 68.  Subtract 10.

Put a screenshot of your completed hundred chart here:

0. Reflect by answering each of these questions::

a. How does the structure of the hundreds chart support children in understanding our number system?

b. Look back at your completed hundred charts.  

i. What pattern do you notice when adding one?  What pattern do you notice when subtracting one? 

ii. What pattern do you notice when adding ten?  What pattern do you notice when subtracting ten?

c. How can these patterns help you whenever you are adding/subtracting 1 or adding/subtracting 10?

d. How does the hundreds chart help students relate adding one and subtracting one to the counting sequence? 

e. How does the hundreds chart help students relate adding ten and subtracting ten to the counting sequence?

Reasoning Strategy 2 – Doubles:  Students tend to learn their doubles facts quickly (0+0 through 9+9).  These facts can then serve as anchors for other facts (e.g., knowing 3+3 helps a student add 3+4).  To promote learning of these facts, teachers should provide ample “doubling” activities.  This can be done with read alouds, story problems, or picture cards (show a picture of a tricycle and ask, “how many wheels on two tricycles?”).   

1. Watch this video of the book
Two of Everything
.  Pause to answer each question:

· (2.21)  How many coins does Mrs. Haktak have now?  Write an expression to represent the amount (e.g., 2+2).

· (2:40)  How many buttons were on the two coats in all?  Write an expression to represent the amount.

· (3:09)  How many coins do Mr. and Mrs. Haktak have now?  Write an expression to represent the amount.

· If we put a spider in the pot, how many legs would there be in all?

· If we put a duck in the put, how many legs would there be? 

0. Reflect:

  Write a “doubling” word problem for the expression 4+4.

Reasoning Strategy 3 – Combinations of 10:  In the early grades, students work with ‘both addends unknown’ problems to explore combinations of ten.  As students solve these problems by decomposing (breaking apart) and composing (putting together) ten, they begin to commit these facts to memory. 

NOTE:  Use this

virtual rekenrek

to work with this task. Watch

this video

on how to decompose numbers on the rekenrek.

1. Use a rekenrek to solve this problem. Attach a picture of the virtual rekenrek below. 

Adapted from Cumberland County Schools Meaningful Math Tasks.

0. Reflect by responding to these questions:

a. Which combination of 10 did you start with? How did you (or could you) use this combination of 10 to find other combinations?

b. Why was the rekenrek selected as an appropriate tool for this task? Specifically, how does it support student thinking and serve as a visual model?

c. Is ‘4 and 6’ the same as ‘6 and 4’?                           (We’ll discuss this later in the assignment.)

Reasoning Strategy 4 – Anchoring 10/Making 10:  The making 10 strategy builds from students’ knowledge of the combinations of ten.  This strategy is most useful when one addend is close to 10 (e.g.,
8
+6  or  4+
9
). 

1. Watch
this video
to learn about the making ten strategy.

0. Reflect on the video:

a. Which addition fact does this video represent?

b. What is the same? What is different?

0. Make a video showing how to add 9+6 using the making 10 strategy.  Post a link to your video here. 
***Do not skip this question*** It is weighted heavily and you need practice. 

1.

Reasoning Strategy 5 – Near Doubles: Students tend to easily remember their double facts (e.g., 4+4).  Teachers can help students use what they know about doubles to solve closely related facts (e.g., 4+5 and 4+3).   

1. Play the online math game
Break Apart
.  (Click
addition
. Click
doubles – easy
.)

0. Reflect:

a. How does the game Break Apart apply students’ knowledge of doubles facts to solve near doubles facts?

b. Using the approach shown in Break Apart, explain how you would solve 7+8.

Reasoning Strategy 6 – Properties of Operations: When students understand the properties of operations, they can use this understanding to efficiently and flexibly add and subtract.  For example, many students attempt to remember each addition fact in isolation.  When learning about the commutative property, students realize by mastering one fact they have really mastered two facts (e.g., 2+3 = 3+2).  

Note: When working with the commutative property, students should realize the difference between “same” and “same amount as”.  For example: In Rahsan’s candy problem,
4 yellow candies and 6 red candies
is the same amount as
6 yellow candies and 4 red candies
.  However, these groupings don’t look exactly the same.  

When introducing properties of operations, the focus should not be on memorizing property names and definitions.  Rather, students should make observations when working with the operations, discussing what they notice and wonder.   

1. Watch these videos:
Video 1

/

Video 2

0. Reflect on the video:

a. What do you notice?

b. What do you wonder?

0. You overhear two students in your class discussing how to solve 2+7:

Leo
: I started by putting 7 in my head.  Then, I counted on two more.  7…8…9.  The answer is 9.

Nora:
You can’t do that!  The problem is 2+7, not 7+2.

How can you help Nora understand that Leo’s method can be used for solving 2+7?  Show your explanation to Nora using pictures and words, or a video clip.  Insert your pictures or a link to your video below.