Week 3: Addition & Subtraction

Class resumed on Tuesday of this week and we continued doing some labeling practice for sets. Some of these practice problems involved shading with parentheses. Here are some of the problems we worked on in class.

1.
Shorthand notation:

 

 

 

Visual:

 

2.

Shorthand notation:

 

 



Visual:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.

Shorthand notation

 

Visual:

 

4.

Shorthand notation:

 

Visual:

 

 

 



For more practice you can use http://nlvm.usu.edu/en/nav/frames_asid_153_g_2_t_1.html?open=instructions&from=search.html?qt=venn .

 

On Thursday we started off working on sets, but instead of labeling that we have been doing, we incorporated variables such as letters found in two names.

 

5.



 

Visual:

 

In this problem the letters common letter in each set are underlined. When putting them into the Venn diagram only need to be written once.

In class we also looked at the properties of addition. The first two were the Set Model of Addition and the Measurement/Number Line/Active Model.

Here is an example of each to distinguish between the two when looking at a word problem.

Example of a Set:

Eroll has seven chocolate chip cookies and eight oatmeal cookies. How many does he have altogether?

Example of a Measurement:

Eroll has seven chocolate chip cookies and bakes eight more. How many does he have in total?

Other properties of addition are:

Commutative Property: A + B = B + A

In this property moving the numbers around in order to make the problem easier to solve.

Associative Property: A + (B + C) = (A + B) + C

Grouping numbers together in different ways

Identity Property of 0: A + 0 = A

When adding zero the number stays the same.

We also looked at Number Relationships in math. These concepts are the building block for students to continue learning math.

Spatial Relationships:

Recognizing how many numbers there are without counting by seeing the visual pattern.

One & Two More or Less:

This is not the ability to count on two or count two back from a number, but instead knowing which numbers are one more or two less than any given number.

Benchmarks of 5 & 10:

Since 10 plays such an important role in our number system (2 5s make 10). Students must know how numbers relate to five and ten.

Part-Part-Whole:

To conceptualize a number as being made up of two or more parts is the most important relationship to develop.

We lastly looked at Models of Subtraction:

Take Away Example:

Eroll has eight dollars. He spends five dollars for a movie ticket. How much money does he have now? (8 - 5 = __ )

Missing Addend Example:

Eroll had five dollars. He found some lying on the ground. Now he has eight dollars. How much money did he find? (5 + __ = 8)

Comparison Example:

Eroll has eight dollars. Kyle has five. How much more money does Eroll have then Kyle?

Number Line/Measurement/Distance Example:

Eroll hiked eight miles. Five were before lunch. How many miles did he hike after lunch?

All of the concepts learned in this week can be applied into the second set of our homework.



Stay tuned for next week's blog and go Cougs!

Week 2: Problem solving & Sets

On Tuesday we finished up the concept of problem solving . On of the problems we focused on during class was a word problem involving find the perimeter a hexagon tiles with 1 centimeter sides. In solving the problems we were challenged to do so with out simply counting and  to use alegrabric ways to find the perimeter as the number of tiles increased.

Starting total:

When looking for the perimeter of a set of 100 hexagons we, as a class, came up with 3 algrebraic ways to solve the problem.

In solving  for the perimeter this way we also reviewed the words of constant (which are highlighted in red in the photos) and variables (the H in the problem).

On Thursday we began learning about sets. In doing so we reviewed the terms; union, intersection, and complement. we went over the shorthand notation and a visual way to represent the set.

Union:
Shorthand notation:

Visual:

Intersection:

Shorthand notation: 

Visual:

Complement:

Shorthand notation:

Visual:

 Shorthand notation:

Visual:

Shorthand notation:

Visual:

We also did an activity in class that helped in practicing labeling and making sets with 2-3 rings and colored shapes called attribute pieces. This activity can be found in our problem solving and mathematical reasoning class activity book on pages 27-40.

In doing this activity we also looked at the difference between "and" & "or" in looking at a set.

Visual for And:

Visual for Or:

Lastly, we began we added a third ring and continued with labeling and making a visual.

Shorthand notation example:

Visual:

If the concept of set is confusing there is no worry on Tuesday of next week we are continuing working with sets. This concept is important to grasp and understand since the will be found in our homework for set 2.1.

Stay tuned for next posting and Go Cougs!

 

Week 1: Subtraction

Hello commenters, welcome to my math 251.2 math blog. My job this unit is to update you all on all the math concepts learned in Neil 5W. Here is an overview on this week’s concepts.

Tuesday was our first day of 251 starting of second semester. We went over the syllabus and we were introduced to our fellow peers and our professor, Christina Tondevold. Our class actives for the week included an array of subtraction problems and analyzing the different problem solving techniques used.

 A majority of us used the technique of borrowing or subtraction by regrouping in finding the answer for the first problems. Christina shared with the class that this technique, although widely taught, is one of the most challenging math techniques to teach and for elementary students to learn.

Throughout the week some of us we were introduced to using a number line in subtraction problems. Using this technique makes the idea of math visual for students, which for young students is an easier approach for them to understand. It also introduces the concept of finding the difference in subtraction and how using this method the solution can be solved by adding. This idea and technique is something I had never considered before this class.

On Thursday we continued with additional simple subtraction problems and later were assigned to complete a word problem involving a collection of beetles and lizards.

In solving the problem Christina discussed the issues of using algebraic methods to find answers. This being that as students, we learn the formulas in algebra and but never the meaning of what the parts stand for on their own. She also had us look at how using a visual method, like drawing pictures, had the same concept as an algebra problem; this too I never considered or saw the relationship before.

Stay tuned for next week’s blog and go Cougs!