Saturday, March 2, 2024

Writer's checklist for research papers

The ultimate writing checklist for research papers

What should be included in a solid writer's checklist before students embark on preparing a research paper or project?


Research papers and projects are essential parts of academics that require critical thinking, extensive research, and exceptional writing skills. Students need to consider many elements before starting their project to ensure they don't miss out on important aspects of their writing. This is where a writer's checklist comes in handy. In this blog post, we'll discuss what should be included in a solid writer's checklist before students embark on a research paper or project.

Let's explore the components of a good, solid checklist

1. Choose a topic

Choosing an interesting topic can make the writing process more manageable and enjoyable. Students should choose, if possible, a topic they're passionate and curious about, ensuring they can find ample resources to support their research. Narrowing the topic down to a specific area will make the research more targeted and easier.

2. Conduct thorough research

After choosing the topic, the next step is to conduct thorough research. Utilize reliable sources such as scientific journals, books, and academic websites to gather information. Students should compile all their sources in a well-organized manner for easy referencing later.

3. Create an outline

A good outline can ensure that the writing process is organized and flawless. It helps students to stay on the right track and ensure all the necessary components of the paper or project are covered. Outlines can be made in bullet points or brief phrases, and they should include the introduction, several main points, and a conclusion.

4. Write the first draft

Once the outline is complete, it's time to start writing the first draft. This draft should not be perfect – it's an opportunity to get all the ideas down on paper. Students should focus on writing without worrying too much about grammar or sentence structure.

5. Edit and revise thoroughly

Revising and editing are critical parts of the writing process. Students should take some time off and come back to their work with a fresh perspective. Revise the first draft, adding or removing information as necessary, and correcting grammatical and spelling errors. It is also advisable to seek feedback from peers, teachers, and/or tutors before submission.


Preparing a research paper or project can be a daunting task, but with a solid writer's checklist, it can be an enjoyable process. By following the tips mentioned above, students can ensure their writing is organized, thorough, and error-free. Writing is an essential skill that students carry through life, and with practice, they can become exceptional writers.

Math word problem practice

Mastering tricky word problems: Nine math problems for middle school students 

Nine math word problems that are somewhat tricky and therefore require close reading, have multiple steps, and are suitable for middle school math students. Correct answers and detailed explanations to those answers are included.


Math can be tough, especially word problems! Word problems test not only your math skills but also your reading comprehension and critical thinking abilities. They are tricky because they require you to break down the problem, identify the important information, and use logical reasoning to solve them. In this blog post, we'll cover nine tricky math word problems that require close reading, multiple steps, and are suitable for middle school students. We've also included detailed explanations for each problem's solution, so don't worry if you feel stuck!

Problem 1: A rectangular parking lot measures 60 meters by 80 meters. If a car uses 4 square meters to park, how many cars can fit in the parking lot?

Answer: 120 cars

Explanation: To find out how many cars can fit in the parking lot, we first need to know the total area of the parking lot. To do so, we multiply the length and width: 60 meters × 80 meters = 4,800 square meters. Then, we divide the total area by the area a single car uses: 4,800/4 = 1,200. Therefore, 1,200 cars can fit in the parking lot.

Problem 2: In a class election, there are 30 students. The winner needs more than half of the votes in order to win. If 16 students voted for Student A, and the rest voted for Student B, how many students voted for Student B?

Answer: 14 students

Explanation: To find out how many students voted for B, we first need to know the total number of votes. Since half of the votes are 15, any number above 15 will be the winning number. We already know that 16 people voted for Student A, so if the class has 30 students, then 30 - 16 = 14 students voted for B.

Problem 3: There are 5 red balls, 9 blue balls, and 7 yellow balls in a bag. What is the probability of grabbing a red ball first and then a blue ball?

Answer: 5/63

Explanation: There are five red balls in the bag, so the probability of grabbing one on the first try is 5/21. There are now 20 balls remaining (9 blue and 7 yellow), so the probability of grabbing one blue ball is 9/20. To find out the probability of grabbing a red ball first and then a blue ball, we multiply the probabilities of each event together: 5/21 × 9/20 = 1/63. Therefore, the probability of grabbing a red ball first and then a blue ball is 5/63.

Problem 4: The difference between two numbers is 35. If one number is 57, what is the other number?

Answer: 22

Explanation: Let's call the other number we're trying to find "x". We know the difference between the two numbers (57 and x) is 35, so we set up the equation 57 - x = 35. Next, we isolate "x" by adding 35 to both sides of the equation: 57 - x + 35 = 35 + 35. Simplifying the equation gives us: 92 - x = 70. Then, we subtract 92 from both sides to solve for "x": 92 - 92 - x = 70 - 92 or -x = -22. Finally, we divide -22 by -1 to isolate "x": x = 22.

Problem 5: A sphere has a radius of 3 cm. What is its volume?

Answer: 113.1 cubic centimeters

Explanation: To find the volume of a sphere, we use the formula V = 4/3πr³, where "V" stands for volume, "π" represents Pi (3.14), and "r" represents the sphere's radius. Substituting the given radius (3 cm) into the formula, we get V = 4/3 x 3.14 x (3 cm)³. Simplifying the equation results in V = 4/3 x 3.14 x 27 cm³ or V = 113.1 cm³. Therefore, the volume of the sphere is 113.1 cubic centimeters.

Problem 6: A pear-shaped swimming pool has a deep end and a shallow end. The shallow end of the pool is 3 meters deep and is 10 meters wide and 15 meters long. The deeper region of the pool is 6 meters deep and is conical in shape. The diameter of the deeper section is 10 meters and slants down to meet the shallow end smoothly. What is the total surface area of the pool?

Answer: 628.96 square meters

Explanation: First, we need to find out the volume of the deep section of the pool. Since it is conical in shape, we use the volume formula for a cone: V = 1/3πr²h, where "r" represents the radius and "h" represents the height. We find the radius by dividing the diameter (10 meters) by 2, which gives us 5 meters. Next, the height of the conical section is calculated by subtracting the height of the shallow end (3 meters) from the depth of the deep end (6 meters), resulting in 3 meters. Substituting the values into the formula gives us V = 1/3π(5)²(3), which is approximately equal to 78.54 cubic meters. Next, we need to find the total surface area of the pool. To do so, we calculate the area of the bottom of the pool (10 meters x 15 meters) and add that to the lateral area of the deep section of the pool (by using the formula πrl). We can find "l," the slant height, by using the Pythagorean theorem: l² = r² + h², where "h" is the height of the cone and "r" is the radius. Substituting the values gives us l² = 5² + 3² or l² = 34. Since we only need to know the area of the slant side, we can ignore the square root and use l = √34. Thus, the surface area is calculated as: 10 x 15 + π(5) x (√34). Plugging in the numbers, the total surface area of the pool is approximately 628.96 square meters.

Problem 7: 2/3 of Tom's marbles are blue, and 19 of them are yellow. If Tom has 87 marbles, what is the total number of marbles that are not blue?

Answer: 29 marbles

Explanation: If 2/3 of Tom's marbles are blue, then 1/3 of his marbles are not blue. Since the total number of Tom's marbles is 87; therefore, 1/3 of that is (87/3) = 29 marbles. Therefore, Tom has 29 marbles that are not blue.

Problem 8: There are 22 boys and 18 girls in a class. If one is selected randomly, what is the probability that the selected student is a boy?

Answer: 55%

Explanation: There are a total of 40 students in the class (22 boys + 18 girls). The probability of selecting a boy is the number of boys divided by the total number of students in the class. Therefore, 22/40 = 0.55, which is 55%.

Problem 9: A recipe calls for 2 1/2 cups of flour. If Mark only has a 1/4 measuring cup, how many times does he need to fill it up to get the required amount?

Answer: 10 times

Explanation: Mark needs 2 1/2 cups of flour. Since he only has a 1/4 measuring cup, he needs to fill it up multiple times until he has the required amount of flour. To figure out how many times he needs to fill up his measuring cup, we convert 2½ cups to the same measuring unit as the measuring cup (in this case, ¼ cup). Therefore, 2 ½ cups is equal to 10 quarter-cups, so Mark needs to fill up his measuring cup 10 times.

If you found this post helpful, you may also want to check out our posts on math operations vocabulary, solving one-step math equations, and solving two-step math equations.

Wednesday, February 28, 2024

A different kind of family tree - a poem


In this 11-stanza original poem turned in as an assignment in February 2024 as part of my pursuit of a master's degree in theology, I reflect on Hebrews 11 largely from the interpretation that we are all invited to join a different kind of family tree – a different kind of genealogy or pedigree, one linking us by faith and ultimately by the blood of Christ back through the Old Testament, back to the “Faith of the Ancients,” as this specific chapter/pericope is titled. I end with the universal call by Vatican II that all the faithful are called to be priests, prophets, and kings.

I chose to incorporate a rhyming scheme which follows an ABBA pattern, meaning that the first and fourth lines in each stanza rhyme, while the two lines sandwiched in the middle follow their own rhyming pattern. In my research and thought process for determining rhyming words, I relied heavily on the reference tool available at Rhyme Zone (, as well as on occasional Google searches for synonyms.

“A different kind of family tree”

Inspired largely by Hebrews 11 – “Faith of the Ancients”

Aaron S. Robertson

You’re invited to be a part of this,
A different kind of family tree,
One truly as wide and adventurous as the sea,
An invite you surely don’t want to miss.

All are welcomed to join this one,
A family not necessarily all tied by blood,
It may sound strange, but it’s one united by a flood,
Come to believe in the Word, and it is done.

That comment about blood we’ll come back to a little later,
Because we do in fact all share that common link,
It was shed by the One on the cross who would save us from the brink,
By He whom on this entire earth no one can ever be greater.

An open invite to join along and receive immense grace,
He wants this for you, the question is will you say, “yes,”
You were born for greatness, so do not settle for anything less,
All your offenses and mistakes our common Father will erase.

Like all families, this one has bickering and many a fight,
All the emotions are surely here,
Joy, confusion, anger, sorrow, and fear,
There’s plenty of darkness but in the end even greater light.

Joining this lineage guarantees an audacious quest,
With the help of this your family you’ll defeat the abyss,
So that in the end you’ll know nothing but lifegiving bliss,
After all the tribulation a beautiful and eternal rest.

At times you’ll wonder how you’ll ever cope,
But do your homework as would any good sleuth,
And you’ll find here that you’re on the path to enlightened truth,
In all the trying moments, you’ll be washed over by hope.

This family already has a known beginning and end,
Wrapped in the warmth of a different kind of sun (Son),
Indeed, by He who is the promised one,
Our Father, our provider, our Savior, and our friend.

You’ll come to realize that this family is the best,
So many to look up to and emulate,
They’ll help you keep on the narrow and straight,
With their help and the mercy of our God you’ll always be blessed.

At times, you’ll suffer immensely as you walk along desert sand,
But cling to your faith on this difficult trek,
Though at times it will feel like you’re headed toward a horrible wreck,
Indeed, your destination is His promised land.

With this kind of faith, through Him you can do all things,
Mountains can move, hardened hearts softened, and walls torn down,
Martyrdom for Him, if necessary, will result in an eternal crown,
In the end, we’re all called to be priests, prophets, and kings.

Monday, February 26, 2024

Joy in Philippians

Aaron S. Robertson

When it comes to the overall theme of joy in Philippians, 4:6-7 really resonates for me as it relates to my own return to, and understanding of, the faith: "Have no anxiety at all, but in everything, by prayer and petition, with thanksgiving, make your requests known to God. Then the peace of God that surpasses all understanding will guard your hearts and minds in Christ Jesus."

What greater joy can there ever be once we truly make that connection with God while still in this life? What greater joy can there ever be than truly experiencing the reality of God? Than knowing that God is in our lives, He wants to be in our lives, and He wants us to share in His life? Than knowing with absolute conviction that this life isn't all there is? That something far, far more beautiful beyond our limited comprehension awaits us, if only we give it an honest chance by trying to meet God halfway and allow Him to do the rest? I've been so wonderfully blessed to make this connection with this reality, and, indeed, there is a peace residing in my mind and deep within my heart now that cannot be explained by anything in this world.

Paul's words in Philippians 4:6-7 also remind me of Andrew's reaction portrayed in season 1, episode 4, of The Chosen, once he has met and recognized the Savior. In describing his encounter with Jesus to his brother, a skeptical and stubborn Simon Peter, the sheer joy reflected on Andrew's face and in his words really resonate. While Simon Peter is too focused on what he feels are bigger issues at that moment, Andrew, filled with joy, is trying to tell him that none of it matters.

Suffering in 2 Corinthians

Aaron S. Robertson

Paul states in 2 Corinthians 1:3-4, "Blessed be the God and Father of our Lord Jesus Christ, the Father of compassion and God of all encouragement, who encourages us in our every affliction, so that we may be able to encourage those who are in any affliction with the encouragement with which we ourselves are encouraged by God."

This passage, I believe, does a wonderful job of succinctly explaining how we are each to unite our own suffering to the suffering of Christ and to one another. The passage brings the theme of suffering full circle in that our Father is always there to encourage and console us in our every struggle. In turn, as our Father is always there for us, we are able, and indeed expected, to be a source of comfort and understanding to others in their own sets of circumstances. Suffering helps each of us grow in virtue. It helps us not only to cling to God as individuals in our own unique time of need, but it also strengthens our bonds with our fellow brothers and sisters in God by helping us relate to what others are going through. As our Father shows mercy, compassion, and encouragement to each one of us, we are, in turn, equipped to do the same for others.

Paul closes the loop to this full circle in the next two verses, 2 Corinthians 1:5-6, when he writes, "For as Christ's sufferings overflow to us, so through Christ does our encouragement also overflow. If we are afflicted, it is for your encouragement and salvation; if we are encouraged, it is for your encouragement, which enables you to endure the same sufferings that we suffer."

In short, suffering brings us closer to God and to one another as fellow human beings; as fellow children of our Father adopted through Christ. One can easily see how this all ultimately relates back to our commandment to love one another - to will the best for each other.

The Call of the Disciples in The Chosen

Aaron S. Robertson

Author's note

What follows is a recent assignment (February 2024) for my New Testament class in pursuit of a master's degree in theology from Sacred Heart Seminary and School of Theology. For the assignment, we were to pretend a friend had e-mailed us after watching an episode of The Chosen (specifically Season 1, Episode 4), wanting to know what really happened when Jesus called His disciples and asking how we should account for differences in the story line among the four gospel accounts. Trying to be somewhat humorous with my love for Roman names, my imaginary friend here is named Sixtus, after five popes with that name. For reference, The Call of the Disciples is found in Matthew 4:18-22; Mark 1:16-20; Luke 5:1-11; and John 1:35-51.


It’s wonderful to hear from you. It’s been a little while – I hope you’re doing well. I’d be more than happy to try to help you understand what may be going on between the four gospels and what you saw play out in the episode of The Chosen you referenced. I know one of the big questions on your mind is whether Peter really dropped to his knees crying and telling Jesus to depart from him for being such a sinful man. There’s a lot to unpack here, and I’ll certainly do my best.

Episode 4 of season 1 of The Chosen, called “The Rock On Which It Was Built,” portrays the calling of the first disciples. This event is portrayed differently in each of the four gospel accounts; in some cases, very differently. It appears that The Chosen episode attempts to blend all four accounts into one, cohesive narrative. Let’s explore this further.

To begin, Matthew’s and Mark’s accounts, while largely the same and the two that are most identical out of the four, have some subtle differences. For example, in Matthew 4:22, there is no mention of hired servants in the boat with James, John, and Zebedee. Mark 1:20 mentions the presence of hired servants. In Matthew 4:18, Simon is also called Peter. Mark 1:16 has no mention that Simon is also called Peter.

Now, Luke’s and John’s accounts are very different from Matthew’s and Mark’s, and contrast sharply from one another. Let’s begin with Luke and some of the more minor nuances within Luke as compared to Matthew and Mark. In Luke 5:1-11, Simon is referred to as or called “Simon” three times before arriving to verse 8, which then calls Simon “Simon Peter.” This may lead to some confusion for those reading this gospel account for the first time without knowing that Simon and Peter are the same person. Additionally, rather than the Sea of Galilee being the setting (as in Matthew and Mark), the setting in Luke is the “lake of Gennesaret.”

Let’s now turn our attention to the major differences in Luke compared to Matthew and Mark. Luke has Jesus teaching a crowd from the boat; instructing Simon to attempt one more catch, which, as we know, produces an overly-abundant yield of fish; dialogue from Simon that is exclusive to Luke’s telling of the account (This is where your question about Peter falling to his knees comes in); and has James and John with Simon in the same setting (instead of Jesus approaching them a little further down the road as in Matthew and Mark), specifically naming James and John as fishing partners of Simon. There is no mention of Simon’s brother, Andrew, in Luke’s account! Also, Luke mentions that James and John are sons of Zebedee, but he does not place Zebedee at the scene fishing with his sons.

John’s account (1:35-51) begins by mentioning John the Baptist and how he pointed out the Messiah to Andrew, who is a disciple of John the Baptist, along with another one of his disciples. Andrew, excited about seeing and recognizing the Messiah (Jesus), goes to tell his brother Simon all about it. This is conducive to what happens in The Chosen episode, where Andrew excitedly shares with Simon that he came across the Messiah while he was with John the Baptist. The episode does not have Simon responding enthusiastically, as we know. Simon is too focused on what he feels are bigger issues at that moment, while Andrew, filled with joy and hope, is trying to tell Simon that none of it matters – the Romans, none of it. For the Messiah has come!

Wow, hey? This is certainly a lot to take in, I know. All four gospels have differences. Some, as we see, are very different. As I said a while ago, it looks like The Chosen episode attempts to skillfully blend all four accounts into a unified, cohesive narrative. In the episode, we get Andrew joyfully sharing the good news with Simon after Andrew spots the Messiah while with John the Baptist (John’s gospel). From there, we see the major elements of Luke’s gospel play out – we see Jesus teaching a crowd from the boat; Jesus instructing Simon to attempt that one last catch; there’s the dialogue from Simon, which, again, is exclusive to Luke’s account; and James and John are with Simon in the same setting. We then turn to Matthew’s and Mark’s accounts – Andrew is in the scene, along with Zebedee, but there doesn’t appear to be the hired servants specific to Mark’s (1:20) account.

How can all this be, you’re wondering? How can there be four different versions of the calling of the first disciples, and what amounts to essentially a fifth account created for television? What really happened? Are we getting the truth? Did Simon really fall to his knees, crying and asking Jesus to depart from him for being such a sinful man? We need not fear any of the answers to these and similar questions, and here’s why.

According to the Historicity of the Gospels, a document published in 1964 by the Pontifical Biblical Commission (PBC), “The truth of the Gospel account is not compromised because the Evangelists report the Lord’s words and deeds in different order. Nor is it hurt because they report His words, not literally but in a variety of ways, while retaining the same meaning” (II. The Elaboration of the Gospel Message: Order of Treatment). Ultimately, what we must remember here, Sixtus, is that accounts of the life of Jesus, His teachings, the works of the Apostles, and so on, were originally handed down orally. It wasn’t until later that,
…many attempted “to draw up a narrative” of the events connected with the Lord Jesus. The sacred authors, each using all approach suited to his specific purpose, recorded this primitive teaching in the four Gospels for the benefit of the churches. Of the many elements at hand they reported some, summarized others, and developed still others in accordance with the needs of the various churches. They used every possible means to ensure that their readers would come to know the validity of the things they had been taught. From the material available to them the Evangelists selected those items most suited to their specific purpose and to the condition of a particular audience. And they narrated these events in the manner most suited to satisfy their purpose and their audience’s condition. (II. The Elaboration of the Gospel Message: The Four Evangelists)
Finally, I direct you to paragraph 19 of Dei Verbum, a dogmatic constitution approved and published in 1965 by the Second Vatican Council, which reads, in part:
Holy Mother Church has firmly and with absolute constancy held, and continues to hold, that the four Gospels just named, whose historical character the Church unhesitatingly asserts, faithfully hand on what Jesus Christ, while living among men, really did and taught for their eternal salvation until the day He was taken up into heaven. (Chapter V: The New Testament, para. 19)
In short, my friend, the fact that the four gospel accounts have at times very noticeable differences in details, the ordering of events, etc., is nothing to fear. We trust that the Holy Spirit guided each of the evangelists in writing down these accounts faithfully and with specific churches, audiences, and other relevant circumstances in mind. None of this detracts from the truth. The Chosen does a wonderful job of combining multiple gospel accounts into one, easy-to-understand narrative for a mass audience.

I hope this all helps, Sixtus! Great to hear from you, my friend. Please don’t hesitate to reach out to me with any additional questions or concerns you may have, and I’ll certainly do my best to address them.

All the Best,


Friday, February 9, 2024

Math operations vocabulary

Following are a couple helpful videos on basic math operations vocabulary. You'll also find written lists under the videos. Between the videos and the lists, this is a good sampling of common vocabulary terms you'll always come across as you do a variety of math problems and math operations.

Math Vocabulary Words for Addition and Subtraction!

Math Vocabulary Words for Multiplication and Division!

  • Altogether (or all together)
  • Join
  • Increase
  • Add
  • Combined (or combine)
  • In all
  • Sum
  • Both
  • Difference
  • Left
  • Decrease
  • Take away (or take)
  • Fewer
  • Subtract
  • Minus
  • Equal groups
  • Altogether (or all together)
  • Twice
  • Groups of
  • Per
  • Double
  • Multiply
  • Each
  • Times
  • Each
  • Divide
  • Divided by
  • How many in each group
  • Half
  • Cut up
  • Between
  • Share