Entry # 10 Measurement & Data: Work with money (2.MD)

Personal Objective: This week I spent time looking at the basics of working with money at the 2nd grade level. My goal was to gather visual references that could be used to breakdown and express the many ways pennies, nickels, dimes and quarters can be combined to build different monetary amounts.

Common Core Standard:

2nd Grade: 2.MD

Work with money

8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

Resources/Tips:

https://www.carsondellosa.com/114281--identifying-us-money-chart-grade-k-3-114281/

https://business.wikinut.com/Alt-codes-you-may-need/3ejp39s5/

100 Pennies = 1 Dollar

20 Nickels = 1 Dollar

10 Dimes = 1 Dollar

4 Quarters = 1 Dollar

http://bluebirdplanet.com/education_extras/us_money.html

Activities/Worksheets: 

https://www.greatschools.org/gk/worksheets/money-word-problems-2/

http://www.primarythemepark.com/2016/02/money-activities-for-second-grade/

Reflection: Having an understanding of working with money in its most basic sense is something that can be easily taken for granted as an adult. In reviewing and breaking down this area it wasn't hard to recognize the initial challenges that pennies nickels, dimes and quarters can present to students when exploring the various combinations that can be built with them. I think that clear visual representation and hands on activities are the best ways to teach about how money works. I also love that historical figures like Lincoln, Jefferson, Roosevelt and Washington can be tied into this area of study as students analyze coins. Working with money is a skill that students need to have a firm understanding of because they will without a doubt draw upon for the rest of their lives. 

Entry # 9 Operations & Algebraic Thinking: Represent and solve problems involving addition and subtraction. (1.OA)

Personal Objective: This week I concentrated on how to represent and solve problems involving addition and subtraction at the 1st grade level. My goal was to organize, create and compile visual and tactile approaches that could be used to teach the elements of addition and subtraction to 1st grade students.

Common Core Standard:

1st Grade: 1.OA

Represent and solve problems involving addition and subtraction.

1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Resources/Tips:

Counters

4 chickens plus 2 chickens equals 6 chickens 

4 + 2 = 6

4 chickens minus 3 chickens equals 1 chicken 

4 - 3 = 1

https://www.pinterest.com/pin/560557484849998638/

Ten Frame

Number Line

https://www.twinkl.co.uk/resource/t-n-113-0-20-number-line-display-banner

https://www.instantdisplay.co.uk/number.html

Helpful song and visual

Activities/Worksheets:

https://www.pinterest.com/pin/47780446023764847/


https://www.sparklebox.co.uk/previews/sb12219-number-line-subtraction-worksheets/


https://www.teacherspayteachers.com/Product/Addition-and-Subtraction-Board-Games-509524

Reflection: I really enjoyed taking the time to compile the various techniques that can be taught to students to solve basic addition and subtraction problems. I kept thinking that the multiple approaches I explored in this post would provide a teacher several ways to differentiate instruction to meet students individual needs. I personally like visual and tactile approaches and found using counters, ten frames or number lines offer great assistance to breaking down the problem that needs to be solved. Teaching students to utilize appropriate tools and strategies empowers them and promotes involvement and application of what they have learned.

Entry # 8 Measurement & Data: Represent and interpret data. (2.MD)

Personal Objective: This week I chose to look at how to represent and interpret data (picture graph and a bar graph) at the 2nd grade level. My goal was to create a clear visual step by step breakdown on how to analyze/collect information through sorting, the use of tally marks and picture/bar graphs.

Common Core Standard:

2nd Grade: 2.MD

Represent and interpret data

10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

Resources/Tips:

PICTURE/BAR GRAPHING & TALLYING

Count items using tally marks

Enter data gathered (bar graph)

Crosscheck your work using manipulitives (picture graph)

How to solve a word problem using the information on the graph:

How many more bananas are there than strawberries?

The graph shows there are 6 bananas and 2 strawberries.

6 - 2 = 4

Answer: There are 4 more bananas than strawberries. 

 Tally Mark Reference

https://www.enchantedlearning.com/math/tally/

Activities/Worksheets:

http://www.jasonyost.me/worksheets/

http://vimms.info/worksheets/

Reflection: What I liked best about taking a closer look at graphing was that the end result is rewarding because the information that has been compiled and sorted stands out so clearly. I think that the use of manipulitives to teach math basics is a fun way to allow students to work through what they are learning hands on. I explored this by mixing up little rubber fruit toys and manually  sorting them by type. Once they were sorted I used tally marks to count them. Lastly, I assembled them onto a bar graph and color coded them. Working through this process gave me better insight to how I might go about teaching the subject matter to 2nd grade students.

Entry # 7 Operations & Algebraic Thinking: Gain familiarity with factors and multiples (4.OA)

Personal Objective: This week I explored gaining familiarity with factors and multiples at the 4th grade level. My goal was to create and gather clear visual and written examples that would make the subject area more accessible and fun for students.

Common Core Standard:

4th Grade: 4.OA

Gain familiarity with factors and multiples

4. Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Resources/Tips:

Factors of 6 (1, 2, 3 & 6) visual breakdown using Goldfish

https://www.teachstarter.com/au/teaching-resource/multiplication-poster-multiples_6/

Factors & Multiples Reference

http://mrsmcgaffin.blogspot.com/2016/09/factors-and-multiples-and-arrays-oh-my.html

Prime Number Chart (1-100)
A prime number is a whole number greater than 1 whose only factors are 1 and itself. 

https://www.splashmath.com/math-vocabulary/algebra/prime-number

Activities/Worksheets: 

https://www.pinterest.com/pin/811070214111304766/

http://www.math-aids.com/Factors/

Reflection: While I feel that I have a clear grasp of factors and multiples it was helpful to start thinking of how I might go about teaching this material at the 4th grade level. Reviewing how to identify prime numbers was definitely a helpful refresher. While I don't always love the idea of rote memorization, when it comes to students learning factors and multiples it has its advantages. This being said, visuals and manipulatives like the Goldfish I used to depict the factors of 6 are helpful in establishing basic concepts when introducing the subject to students for the first time.

Entry # 6 Ratios & Proportional Relationships: Understand the concept of a ratio (6.RP)

Personal Objective: 
This week I wanted to take a look at the basics of Ratios & Proportional Relationships: Understand the concept of a ratio at the 6th grade level. My goal in beginning to exploring this standard was to cover the ideas of comparison between two types of items. As always, I think providing fun visuals  helps to promote understanding when introducing a new concept.  

Common Core Standard:

6th Grade: 6.RP

Understand ratio concepts and use ratio reasoning to solve problems.

1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes.

Resources/Tips:

Determining Ratios
A Ratio is a comparison between two items.
The Ratio of Potato Heads to Aliens is two Potato Heads compared to three Aliens.
(Toy Story 4 came out this week so my kids enthusiasm must be influencing me.)

We can write this in any of the three ways below:

2 to 3

2 : 3

2/3

This video does a great job explains the basic idea of ratios.

Activities/Worksheets: 

Building ratio questions around simple recipe proportions makes the idea relatable.

What is the ratio of sugar to water in the lemonade recipe below?

Answer:

1 to 6

1 : 6

1/6

Worksheet for students to explore their understanding of ratios.

https://www.elementarymathgames.net/6th-grade-ratios-worksheet/

Reflection: While exploring the concept of ratios this week, I wanted to not only provide explanation on what ratios were but to also offer some real life application. The idea of recipes was one of the first things that came to mind. A firm understanding of ratios would help if you had to double a recipe. Keeping in mind that the ratios would need to stay the same as the recipe was multiplied is a good way of crosschecking for accuracy. Upon thinking on it, I found it interesting how often I calculate ratios in my head without thinking of them as ratios, for example when I brew my morning coffee.

The Ratio of tablespoons to oz. is one tablespoon compared to six oz.

1 to 6

1 : 6

1/6

Entry # 5 Measurement & Data: Work with time (2.MD)

Personal Objective: 
This week I chose to look at Measurement & Data: Work with time at the 2nd grade level. My goal in exploring this standard is to create and find clear visual and tactile tools that can be used in order to help students learn how to tell and write time from an analog clock. In addition, I would like to provide resources that depict a clear sense of the difference between a.m. and p.m. along with defining what makes up a minute and an hour.  

Common Core Standard:

2nd Grade: 2.MD

Work with time.

7. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Resources/Tips:

I think the clock puzzle below, belonging to my sons would be a helpful visual and tactile tool for teaching students how to tell time.

-The short hand tells the hour (hour hand)

-The long hand tells the minute (minute hand)

-Both hands move from left to right (clockwise)

There are 24 hours in a day (12- a.m. hours & 12- p.m. hours)

-Analog clocks have the hours 1-12 listed on their face 

-To read the minute hand you must multiplay the number indicated by 5

(below see the example 12:15)

Below is an example of what an hour looks like (11:00 a.m-12:00 p.m.)

Starting with the Hour Hand (short Hand) on the 11:00am and moving clockwise:

Minute hand on 12 = 11:00 a.m.

Minute hand on 1 = 11:05 a.m.

Minute hand on 2 = 11:10 a.m.

Minute hand on 3 = 11:15 a.m.

Minute hand on 4 = 11:20 a.m.

Minute hand on 5 = 11:25 a.m.

Minute hand on 6 = 11:30 a.m.

Minute hand on 7 = 11:35 a.m.

Minute hand on 8= 11:40 a.m.

Minute hand on 9 = 11:45 a.m.

Minute hand on 10 = 11:50 a.m.

Minute hand on 11 = 11:55 a.m.

Minute hand on 12 = 12:00 p.m.

You need to know your 5 times table up to 60 in order read an analog clock.

https://www.pinterest.com/ytilford/skip-counting/

Helpful video on the basics of telling time using an analog clock

Activities/Worksheets: 

This worksheet asks students to identify the time indicated on the clock, as well as a.m. or p.m. based on the description included with each question. 

https://www.teacherspayteachers.com/Product/Measurement-and-Data-2nd-Grade-Math-Printables-Worksheets-2123461

This worksheet asks students to draw the hour and minute hand on the face of the clock based on the time that is written below.

http://tagn.info/2nd-grade-telling-time-worksheets/elapsed-time-worksheets-math-time-worksheets-elapsed-time-activities-2nd-grade-telling-time-worksheets-pdf/

Reflection:

I enjoyed the opportunity to breakdown the task of reading the time from an analog clock. I think that it is important to analyze the steps of anything you are going to teach that has become second nature over time. I think something visual and tactile like the clock puzzle I used with the minutes written in the inside ring and the ability to move the hour and minute hands would be a beneficial tool for students beginning to learn the concept of telling time. What I liked most about looking at this part of the Common Core Measurement & Data standard was that it has a clear real life application.

Entry # 4 Number & Operations in Base Ten (1.NBT)

Personal Objective: 
This week I chose to look at half of the Number & Operations in Base Ten Common Core Standard Ten at the 1st grade level. My goal in exploring this standard was to research and create visual aides as well as tactile activities that would provide clear and relatable instruction for 1st graders. I wanted to compile resources that would be fun, stimulating and easy to understand.

Common Core Standard:

1st Grade: 1.NBT (1.-3.)

Extend the counting sequence.

1. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Understand place value.

2. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

a. 10 can be thought of as a bundle of ten ones - called a "ten."

b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six,  seven, eight, or nine ones.

c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

3. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols > , =, and <.

Activities/Worksheets:

In this exercise students would have the opportunity to work with manipulatives. For this example I used Cheerios. Students would be encouraged to build rods and units in two separate groups then make comparisons using a greater than, less than or equal to symbol.

Incorporating a dice game like the one below would provide students with numbers at random to dissect. They would then be asked to represent the selected number with rods and units as well as identify tens and ones. 

https://www.pinterest.com/pin/294282156881414754/

The worksheet below would provide students a chance to test their knowledge of greater than, less than or equal to.

https://www.pinterest.com/pin/184436547211926054/

Resources/Tips:

1-120 Number Line

-Tens and Ones broken down as single digits

-What they represent when they are side by side as one number

https://www.basic-math-explained.com/place-value.html#.XPlUOv1YaUk

Bundle of ten ones - called a "tens/rod."

Singles between tens: "ones/units"

Visual breakdown of two digit place values. 

https://www.pinterest.com/pin/176344141632212349/

Fun way to think about greater than, less than and equal to

https://www.pinterest.com/pin/72550243972102765/?lp=true

Reflection: 
In reviewing the first three points of the Number & Operations in Base Ten Common Core Standards, I found myself reflecting on the importance of a good educational foundation starting in the early grades of elementary school. It seems evident to me that visual reference and tactile tools would be most effective when setting out to teach these basic concepts of mathematics. I especially liked the dice game that prompted students to complete several tasks pertaining to this standard, including mapping the number out and identifying the tens and ones. In addition, I think that utilizing something as simple as Cheerios to encourage students to explore and compare greater than, less than and equal to, provides a simple and familiar tactile experience for students. The alligator trick is also a fun and helpful tool.