Teaching At Home/Addition

Once your student understands counting with manipulatives and identifies where whole numbers fall on a number line, you can add using both of this visuals.  Start with adding 1+1, put out two beans and push the one and one together.  The student should come up with 2.  Have the child count the one and one and then count it again as 2.  Show the numbers with dots on a paper.  One dot plus one dot equals two dots.  Now add 2+1 and move through the same process.

1+1, 2+1. 3+1, 4+1, 5+1, 6+1…

Then add 1+2 and look at 2+1 again to show student that 1+2 and 2+1 gives you the same number of beans or dots.  This is COMMUTATIVE PROPERTY.  Shows that you can add in either direction and get the same thing.

Move to the number line now.  Put your finger or a pencil on the number 1.  Adding one means moving right by one number.  This will also show that 1+1=2.  Show it with beans, dots and number line for several examples.

Go back and ask if 4+5 = 5+4 to revisit commutative property.

Continue to practice single digit addition until student feels confident.

Teaching Math at Home/Whole Numbers


Start with Natural Numbers in another post.  What you will do now is share that Whole Numbers are Natural Numbers plus the number zero.  We don’t learn to count using zero. Explain the zero means nothing. Show a number line at this point.  Have the students use counters (beans, pennies, cubes, etc… under each of the above numbers.  Explain that there are no counters under the zero.  Ask questions to see if student understands the concept of zero.number-line-positive


Teach Numbers at Home/Natural Numbers

Parents and teachers, remember the importance of providing the concrete foundation for numbers. Here is an easy guide to give children a great foundation to:


  1. Teach children how to count aloud.  (1,2,3,4,5,6,7,8,9,10…
  2. Show them what the number look like as they say them.
  3. Show them with number of dots that each number represents. (1. 2: 3:. 4:: 5::
  4. Show them one-to-one correspondence with a manipulative (Something they can touch and hold in their hands- beans, pennies, cubes…)

Work on natural numbers (how we naturally learn to count) for as long as needed in order to gain full understanding.  Ask the child to give you a number to build.

This process gives children something to recall, a picture of in their mind.  This is called CONCRETE.  If students do not have the objects, they can work on the problem by drawing it if necessary.  This is called REPRESENTATION.  Finally using the numbers and symbols, this is the ABSTRACT.  Learning should occur amongst the three forms when learning a new skill. Going straight to abstract without the concrete foundation leaves children to memorize and not truly understand WHAT they are learning.

Beginning with one-to-one correspondence teaches them that each item is counted as one.  This will allow students to learn much more advanced levels when they have the opportunity to build problems with Hands-On materials.


Americans are very generous and donate much and often. I put some lists up on Facebook about good and poor donations. I then started thinking it might be beneficial to share how we processed our donating.

My husband and I set up our Vision, Mission, Value and Goals for our family and business. We run all of our decisions through that filter before we give.

We began with keeping people alive: starving, getting clean water, medications, etc. So as we looked at where to donate to assist with that mind frame, we found that all donations are not created equal which is why you should research places to best donate and those to avoid.

When we couldn’t figure out where our donations really ended up, we decided to work closer to home. We started feeding people ourselves. We started with a small church group. Then my husband decided he wanted to show up alone and make sandwiches for the hungry. What we found then was people abusing that system, not really hungry but just wanting to see what they could get for free.  (We saw this pattern more than once in our hands-on giving which was very disheartening. Made us more concerned about where donations go.)

We then turned to the homeless in our area. Instead of getting involved with others, my husband and son found people on the streets and provided them with sleeping bags. We have learned over time that some homeless people choose not to live in a home. They want to live how they live, they just appreciated the warmth during cold nights.  It was a great way to help others.

Ensuing my passion of teaching, I wanted to assist teachers. Reaching students is the greatest gift a teacher can have in this world. After many years in the classroom, I felt that I had much to offer others in streamlining their workload.  My goal was to help others keep their fire in teaching.

I  wanted to help teachers with the basics of mathematics via workshops on hands-on tools for teaching mathematics. Helping others discover best teaching practices in mathematics was very beneficial to teachers as well as teachers. Sharing the importance of utilizing manipulatives for concrete to representational to abstract interaction to create better student understanding and putting it into long-term memory was the foundation of this work.

As we watched my son struggle as an high-functioning-ADHD student in the public school system, we next set up ADHD conferences along with a psychologist for teachers and parents separately. This turned into an incredible long-term relationship with those in attendance. Parents and teachers alike loved what they learned about this Learning Disability that affects so many. Understanding how to deal with ADHD allows teachers to differentiate instruction to enhance universal learning.

Following, I set up a conference for teachers that wanted to THRIVE and not merely SURVIVE the classroom. This is  where I shared my 28 years of classroom experience to assist teachers with making the best use of time. Classroom management simplified leads to more time to create and work with students.

Next was an ADHD preparation for students called “Starting Off on the Right Foot.  We helped students and their parents prepare for the school year.  We shared what worked in the past and what each had to do to be responsible for their success in the classroom.  We set them up with folders, ways to take notes, using their phone, pencils, pens and more. Parents understood more about what teachers expected in the classroom and what they could do to support their children in the classroom.

All conferences went wonderfully and given at no profit.  I knew exactly where the donations were going and was thrilled with the outcomes.  This is a way to donate hands-on.

Further on, I opened a not-for-profit online school that offered courses for high school students. This morphed into an avenue for highly-motivated students to take courses not offered by their school and courses that allowed students to accomplish school-offered courses in order to take more courses throughout their school years.  It was exciting to be working with students again.

We donate to Christian Radio Stations as we appreciate all the ears that fall upon this music and messages.  We donate to people that directly affect our lives in a positive fashion. We donate to schools where friends and family work or attend. We donate to the cancer society directly through those affected by cancer. We tithe and donate to all of our churches. All of this COULD save lives which gets us back to our hearts desire.

After many trials, we narrowed donating money where it best meet the needs we want to see fulfilled. Currently we donate to leaders in and out of education that we personally know will do what is best. Leaders that follow our vision and mission. Leaders that share with us how others benefitted from the donation. This is how we suggest all to donate.

When you donate to a large organization, you have no idea where that money goes.  If you give a dollar or two at the check-out of a store, where does it go? It’s easy to drop a check into an pre-addressed envelope, but where does it go? Are you helping those in need or is it going into someone’s pocket?

It may take a little time to figure out what your passions are, but make your dollars count for those with needs. Your church is best place to donate above tithing.  Listen for the needs and then match it to your passion. Next, look at the teacher of your children or grandchildren. Look at the places these children are involved.  All of these things will directly effect people you love.

So, before you write that next check, consider if you know exactly where this money goes and whom it will assist.

Happy giving!


Stats about High School and College Dropouts

Eye-Opening Stats about High School and College Dropouts

Guest blog post by Chad Aldeman

With Congress busy debating the future of federal education policy, here’s a thought-provoking statistic: American adults in the 1940s had about the same odds of being a high school graduate as today’s Americans have of being a college graduate.

Beyond the pure shock value of this dramatic shift, it begs the question of whether the two rates will grow at the same rates. Will we boost college attainment rates in this century as fast as we increased high school attainment in the last century?

So far, they’re relatively close mirrors of each other. In 1910, 13.5 percent of American adults had a high school diploma. Forty years later, that figure had risen 21 percentage points. In 1975, 13.9 percent of American adults had a bachelor’s degree. 38 years later, that figure had risen 18 percentage points.

The graph below shows how these two trend lines look remarkably similar. The key question is what will happen next.

chad college-hs completion


We already know what happened to high school attainment rates. We shifted from relatively slow progress through the first half of the 1900s into a much faster rate of growth between 1950 and 1980. In those 30 years, the percentage of American adults with a high school diploma or GED (General Education Diploma) doubled from 34.3 percent to 68.6 percent. Today we’re inching toward 90 percent of our adult population with a high school diploma or GED.

There are still schools with low graduation rates, but even those are falling fast. Nationwide the number of dropout factories—high schools with a graduation rate under 60 percent—declined from more than 2,007 in 2002 to 1,146 in 2013. Similarly, the number of students enrolled in those dropout factories plummeted from 2.6 million to 1.1 million, even as the total student population nationwide increased.

As I show in a new report for Bellwether Education Partners, rapid progress at the high school level, combined with very slow progress in postsecondary education, has led to dramatic changes in our society. And in 2009, the U.S. passed an almost-inevitable milestone: There are now more American adults who have dropped out of college than have dropped out of high school.

chad more college hs dropouts


In pure, raw numbers, college dropouts are now a bigger problem than high school dropouts. Today there are 29.1 million college dropouts versus 24.5 million Americans with less than a high school diploma. It’s safe to predict that this trend will only accelerate as older generations with lower educational attainment rates are gradually replaced by new generations with higher attainment rates.

A number of factors contributed to these changes. In the labor market, employers send a powerful signal that they value candidates with higher levels of education. Individuals are more likely to be employed, and to earn higher wages, for higher levels of education. Compulsory attendance laws played a role too, accelerating high school attendance and completion rates. The introduction of the GED began as a way to offer returning World War II veterans a path to a high school diploma without having to go back to high school. Over time, it took on an even bigger role for other groups of high school dropouts. There are now 6 million Americans with a high school equivalency degree like the GED. That alone accounts for about 3 percent of the increase.

More recently, No Child Left Behind forced schools and districts to start paying attention to high school graduation rates. Those accountability mechanisms helped kickstartanother push to get all students through high school, a reform that has particularly paid off for low-income and minority students and for students with disabilities.

Will college attainment rates keep making slow but steady progress, as they have over the past 40 years, or will we start to see faster growth like we did for high school attainment rates? In my recent paper, I argue that enhancing high school policies could be one lever for policymakers. If states truly held high schools accountable for what happens to their students after graduation, they would build robust portraits of high school quality that measured things like advanced high school course-taking rates, student engagement, and student outcomes in college and careers. All of these steps would ease the transition from high school into college.

But we shouldn’t let higher education institutions off the hook for oversubscribing students to remedial courses or for failing to graduate large portions of their students. It’s an open question whether we’ll make the equivalent policy adjustments in higher education as we did in K-12: will someone create a “GED for college” or will we start holding colleges accountable for their graduation rates to boost education attainment? The answers to these questions matter both to the individuals graduating today and to our broader society going forward.

Chad Aldeman is an Associate Partner at Bellwether Education Partners and the author of “Mind the Gap,” a new report making the case for re-imagining the way states judge high school quality.

Best Jobs for 2017: College Degree Not Necessarily Required

Plumbing, HVAC repair and electrician are three of the hottest job fields for 2017. (Thinkstock)

WASHINGTON — The professions expected to show one of the biggest job growth rates in 2017 and the largest growth in sheer number of jobs will be trade skills, according to a year-end report from CareerBuilder and labor market data provider Emsi.

The U.S. economy is expected to add just over 1 million new jobs in fields such as electrician, plumber and HVAC technician in 2017. That’s a job growth rate of 8 percent. The average hourly earnings for professionals in those fields will be $21.38, or about $45,000 a year in 2017, the report says.

While skills trades generally don’t require a college degree, they do require significant training, through apprenticeship programs and both in-class and on-the-job experience.

The professional category that will show the largest job growth rate in 2017 will be information technology. CareerBuilder says that field will add 472,000 jobs next year, for a growth rate of 12 percent. In demand jobs in that field will include data scientists, user interface developers and mobile software engineers.

Business and financial operations, health care and sales also make CareerBuilder’s list of the five top professions for job growth and opportunities in 2017.

“Our research shows that employers are very invested in expanding head count in areas such as analytics and data science, product development and sales as they strive to stay competitive in B2B and B2C markets,” said CareerBuilder CEO Matt Ferguson.

“Skilled laborers will also see high employment demand in the year ahead as will workers in clinical roles,” he said.

CareerBuilder and Emsi used a variety of national and state employment resources as well as online job postings to come up with their list of 2017’s best jobs.  The full list is below:


(Courtesy CareerBuilder)

Lake Havasu City is looking for educators!

Lake Havasu City is in need of one Administrator at District Office Level, 25 Certified, 21 Classified and 2 Substitutes.  Jobs are currently open for applying. Jobs begin on January 1, 2017.  Looking for a change?  Take a look! ~Sandy

Welcome to the Lake Havasu Unified School District Personnel Department home page. Lake Havasu City, home to the world famous London Bridge, is a growing desert community located in the foothills of the Mohave Mountains in western Arizona on the beautiful Colorado River. We are a community inspired by possibility and rich with promise. Our young city responds to a common purpose: To build a future dependent on our single most precious resource, our youth.

Our school district consists of 6 elementary schools (pre K-6), 1 middle school (7-8), and 1 high school (9-12). Total student enrollment is over 5500 students. We have about 650 staff members with 300 certified positions.

Our mission here in the personnel department is threefold.

  1. To offer an attractive, competitive wage and benefits package.
  2. To market Lake Havasu Unified as a great place to work, and Lake Havasu City as a great place to live.
  3. To help provide a strong support system for our employees.

We are currently accepting applications.

How Well Do You Know the American Constitution

I have kept a constitution test in my “Quizzes for my husband and son” File.

How well do you and your family know the Constitution?  ~Sandy

True or False
1. ______ Our first Constitution was called the Articles of Confederation.
2. ______ Under the Articles of Confederation, Congress had too much power.
3. ______ The first fifteen amendments are called the “Bill of Rights”.
4. ______ Our government is divided into three main branches.
5. ______ The number of articles in the Constitution is seven.
6. ______ There are 21 amendments to the Constitution.
7. ______ Laws for our country may be made only by Congress.
8. ______ United States Representatives have a four year term.
9. ______ Senators have six year terms.
10. ______ The number of representatives a state gets depends on the number of
people in the state.
11. ______ Representatives must be at least 30 years old.
12. ______ Senators must be at least 25 years old.
13. ______ The Vice President serves as Speaker of the House.
14. ______ The number of senators each state gets is three.
15. ______ All impeachments are tried by the Senate.
16. ______ A majority vote makes an impeached man guilty.
17. ______ Congress must meet at least once a year.
18. ______ Senators and Representatives are not paid for their work by the United
States Government.
19. ______ Senators and Representatives may hold no other government jobs while
they are in office.
20. ______ Only the Senate may write tax bills.
21. ______ A bill can never be passed without the Presidentʼs signature.
22. ______ Congress has no power to borrow money.
23. ______ Only the President can declare war.
24. ______ Congress may keep an army for two years at a time.
25. ______ Congress has no power over state militias.
26. ______ A writ of habeas corpus is the same as a bill of attainder.
27. ______ Ex post facto laws may be passed by Congress.
28. ______ Congress has no right to tax products sent from a state.
29. ______ Any state has the right to print its own money.
30. ______ The number of electoral votes a state gets is the same as its number in the
House of Representatives.
31. ______ The President must be at least 40 years old.
32. ______ The President must have lived in the United States for at least 14 years.
33. ______ The President is the Commander in Chief of the armed forces.
34. ______ The President has the power to pardon an impeached man.
35. ______ The President may make a treaty with a foreign country only if the Senate
approves it.
36. ______ The President chooses Supreme Court judges.
37. ______ The President may call Congress together whenever he thinks it is
38. ______ Congress has the power to say what punishment is to be given for treason.
39. ______ United States judges are appointed for life.
40. ______ After amendments have been proposed, they must be ratified by a two
thirds vote in both houses of Congress to become part of the Constitution.
41. ______ An amendment may be made to change the number of senators the states
42. ______ The Constitution is the highest law of our land.
43. ______ All Americans have the right to follow any legal religion they want.
44. ______ The United States Government may take any personʼs property if they can
show a necessity for it, but they must pay for it.
45. ______ In court trials, witnesses against a man must speak when he is there.
46. ______ A person may be tried any number of times for the same crime.
47. ______ A court may give any punishment the judge wishes to give.
48. ______ A state may make a law to keep a person from voting because of his
religion or race.
49. ______ Senators are elected by state legislators.
50. ______ A “writ of habeas corpus” may be suspended in times of war or in cases
where the public safety is involved.
51. People are guaranteed freedom of speech, press, and religion according to the
a. second amendment c. fifth amendment
b. first amendment d. ninth amendment
52. The only amendment to be repealed is the
a. 15th b. 20th c. 18th d. 2nd
53. The number of main branches in our government is
a. 6 b. 21 c. 7 d. 3
54. Congress is divided into
a. 3 parts b. 2 parts c. 4 parts d. 12 parts
55. A Representative in the House is elected to a
a. 2 year term b. 4 year term c. 6 year term d. 8 year term
56. To be a Representative in the House you must have these qualifications
a. live in the state you represent
b. live in the state and have been a citizen for 7 years
c. be 25 years old, live in the state, and be a citizen
d. live in the state, have been a citizen for 7 years, be 25 years old
57. The number of Representatives a state gets depends on
a. the number of voters it has c. the number of Senators it has
b. the number of people it has d. how many they want
58. The Speaker of the House of Representatives is
a. the man they elect c. the Vice President
b. the Secretary of State d. the oldest Representative
59. The power to impeach an officer is given only to
a. the House of Representatives c. the Senate
b. the Supreme Court d. the President
60. Each state gets this number of Senators
a. 1 for every 30,000 c. 2 for each district
b. 3 d. 2
61. The length of a Senatorʼs term is
a. 2 years b. life c. 6 years d. 8 years
62. The Senators are now elected by
a. state legislators c. the state electors
b. the House of Representatives d. the people
63. To be a Senator in Congress you must have these qualifications
a. live in the state you represent
b. live in the state, be 25 years old, and have been a citizen for 7 years
c. live in the state, be 25 years old, and have been a citizen for 9 years
d. live in the state, be 30 years old, and have been a citizen for 9 years
64. All impeachments are tried by the
a. Supreme Court c. Cabinet
b. Senate d. House of Representatives
65. Bills to raise taxes may come only from the
a. Senate c. House of Representatives
b. President d. Cabinet
66. A bill becomes a law without the Presidentʼs signature if
a. two thirds of both houses pass it c. the Senate passes it
b. the House of Representatives passes it d. the Supreme Court passes it
67. A bill which has passed both houses can become a law without the Presidentʼs
signature if
a. the Supreme Court says so
b. the President does not return it to Congress in 10 days
c. the Chief Justice says so
d. the state legislators pass it
68. Taxes may be called for only by the
a. Congress b. President c. Supreme Court d. Cabinet
69. Rules for becoming a U.S. citizen may be made only by the
a. states b. Supreme Court c. Congress d. President
70. Money may be coined or printed only by the
a. Congress c. President
b. Secretary of Treasury d. Secretary of State
71. War may be declared only by the
a. Congress c. President
b. Secretary of Defense d. War Department
72. A writ of habeas corpus is used to
a. impeach the president c. get a man out of jail
b. tell a jury what to do d. ask for an amendment
73. The Constitution forbids the use of a
a. veto b. oath c. preamble d. bill of attainder
74. A law which punishes a man for something not wrong when he did it is called a
a. bill of attainder b. treason c. felony d. ex post facto
75. The Constitution forbids states to
a. make laws b. lay a sales tax c. coin money d. take a census
76. The Constitution forbids Congress to lay a tax on
a. goods sent from one state to another c. liquor
b. goods sent from other countries d. any good sent by ship
77. The number of presidential electors a state gets is
a. the same as the number of Representatives
b. the same as the number of Senators
c. the number of Representatives plus the number of Senators
d. the same as the number of state legislators
78. The qualifications for President are
a. be 35 years old, be a natural born citizen, have lived in the U.S. for 14 years
b. be a citizen, be 35 years old, have lived seven years in the U.S.
c. be a citizen, be 25 years old, have lived 14 years in the U.S.
d. be a natural born citizen, have lived in the U.S. 9 years, and be 30 years old
79. If neither the President nor the Vice President can serve as President, the next in
line is the
a. Chief Justice of the Supreme Court c. Speaker of the House
b. Secretary of State d. Attorney General
80. Treaties made by the President must get the approval of the
a. Supreme Court c. House of Representatives
b. Senate d. people
81. The length of a U.S. government judgeʼs term is
a. 2 years b. life c. 4 years d. 6 years
82. The number of people in the Supreme Court is
a. 8 b. 9 c. 12 d. 15
83. The Constitution guarantees everybody who has done a crime a trial
a. by jury c. in the Supreme Court
b. in the Department of Justice d. in the state of their choice
84. The number of witnesses needed to convict a man of treason is
a. 1 b. 2 c. 3 d. 4
85. A new state may be admitted into the Union only by the
a. Supreme Court c. Congress
b. State Department d. Department of Interior
86. The Constitution guarantees to every state in the Union
a. freedom to make any law it wishes c. legal help
b. a republican form of government d. a pension system
87. To propose an amendment it is necessary to have the agreement of
a. two thirds of both houses of Congress c. the Senate
b. three fourths of both houses of Congress d. the President
88. An amendment goes into the Constitution after it has been ratified by
a. three fourths of the State Legislators c. the Supreme Court
b. two thirds of both houses of Congress d. a majority of Congress
89. No Constitutional amendment could ever change
a. the way we elect the President c. the way Senators are elected
b. equal state representation in the Senate d. the number of states we have
90. Nobody holding a United States office will ever have to pass
a. a Constitution test c. a mental test
b. a religious test d. an age test
91. Congress shall make no law to
a. set voting ages c. establish a draft
b. tax incomes d. set up a religion
92. No personʼs house or property may be searched without a
a. bill of attainder c. search warrant
b. government investigation d. writ of habeas corpus
93. The court may not take a persons life without
a. a circuit judgeʼs agreement c. due process of law
b. evidence of treason d. a confession
94. A person accused of a crime has the right to
a. hear the witnesses against them
b. appeal their case to the Supreme Court
c. have any judge he or she wants
d. be tried wherever they choose
95. The President is elected if
a. they receive a majority of the electoral votes
b. they receive the most popular votes
c. they win the most states
d. they receive the most electoral votes
96. If the candidates for President have no majority of the electoral votes, the
President is elected by the
a. Cabinet c. Senate
b. House of Representatives d. Supreme Court
97. A citizen of the U.S. is a person who
a. owns property in the U.S. c. is white and was born or naturalized here
b. pays taxes d. was born or naturalized here
98. The U.S. can punish a state which denies the right of citizens to vote by
a. fining it
b. reducing its number of Representatives
c. putting it out of the Union
d. reducing its number of Senators
99. How many articles are in the Constitution?
a. 7 b. 21 c. 27 d. 10
100. How many amendments are in the Constitution?
a. 7 b. 21 c. 27 d. 10
MATCHING – Write the number of the amendment that corresponds with the
appropriate amendment.
101. ________ right to bear arms
102. ________ defines citizens and their rights
103. ________ voting age lowered to 18
104. ________ freedom of expression (speech, press, religion, assemble, petition)
105. ________ abolition of slavery
106. ________ right of women to vote
107. ________ income tax
108. ________ repeal of prohibition
109. ________ election of the President & Vice President and who chooses if no
110. ________ limit of presidential terms
111. ________ presidential disability and succession, process for choosing a new V.P.
112. ________ powers reserved to the states
113. ________ prohibition of alcoholic beverages
114. ________ “lame duck” amendment, moves up date of Presidentʼs inauguration
115. ________ direct election of senators by the people
116. ________ powers reserved to the people
117. ________ right of Washington D.C. to vote in presidential election
118. ________ no quartering of troops
119. ________ bail and punishment
120. ________ suits against the states
121. ________ abolition of poll taxes
122. ________ search and seizure
123. ________ a speedy and fair trial
124. ________ civil suits have the right to a jury
125. ________ rights of an accused person, double jeopardy
126. ________ right of black men to vote
127. ________ congressional salaries


Printable Copy

The American Constitution