Singapore Math's focus is on complete student mastery of the topics they will learn about. This is different from many other curriculums that focus on introducing students to many new topics as soon as they are able to. Think going deep vs. going wide. Students are often frustrated by the seemingly easy questions to begin a chapter, but are surprised when the last questions asked are much more challenging and complex. Don't take it easy on the first exercise, make sure they fully understand the material and if they don't set up a time to tutor with me.

Singapore also focuses on mathmatical number sense. This essentially means that students should understand that numbers mean things in the real world and aren't just symbols on a page in mathclass. We are surrounded by numbers in our everyday lives and you would be surprised at how often math sense comes in handy. This math sense helps to give students perspective as they work on new problems and are introduced to new topics.

This is highlighted by every parents favorite questions, word problems and bar models. Although seemingly very complex, these problems test a students (and often our own) comprehension and number sense to a very specific degree. The questions that the curriculum is asking is essentially this, "can this student read this sentence, comprehend what is being asked of them, show how the numbers are related to each other, and discover what is being asked of them?" Many of these word problems have multiple steps, with before and after sections, moving numbers between two models, and other intricate details that can cause frustration and tears. Hopefully, these tools below will help you as you solve these models. I promise, your fourth-grader can solve them, they may just need more encouragement to make it over the frustrating hill that is learning how to work with bar models.

"Struggle with unanswered problems teaches us to tolerate discord with the hope of a solution. We do not give into despair but through struggle develop the virtues of humility, endurance, perserverance, and patience."

It is often difficult to watch our students struggle with not understanding the work they have been assigned, especially when it comes with tears and anger. Yet, we should not encourage them to give into the despair of ignorance, instead we must encourage them on towards the light. If we cave and answer the problems for them, or tell them how to do it, we often do more harm than good. These students must struggle in-order to make this learning their own. If we give them the answers or tell them how to do the problem, we deprive them of their need to struggle. Let us not be so cruel as to show them their are ignorant and leave them there. This begs the question, "Then how do I help them with their homework?" 

The Right Space

Begin by first giving them the right space to work. A loud, messy, and busy place leads to the wrong conditions of the heart and mind. Set aside a place in your home where your students will not be distracted by little ones, the T.V., video games, or cell phones. This is possibly the most difficult first step for families, but it is a surprisingly helpful one. A student with a clean room, is a student with a clean mind. A student with a focused room can have a focused mind. A student with Tik Tok in their hands, is a student who will get very little done.

A Snack

Next, has your student had some kind of snack or light meal to recharge their mind. We forget how often an empty stomach can lead to an empty, grumpy, mind. Encourage them to eat some protein and healthy fats to recover the brain power they expended throughout the day.

Timers

Set a timer short timer for problems that are tough. Have the students entire focus on that problem for two minutes or so. Once the timer is up, have them step away from the table, stretch and maybe color or put dishes away. Have them come back and keep working on the problem as their mind may have been solving it in the background processing that takes place when our brain switches tasks. This timer can also provide a relief and a goal for them to work towards.

Good Questions

Often times, students unintentionally (or intentiaonally) sit, waiting for someone to answer things for them. It is often not malicious, but a learned trait from growing into a young human. This often leads to furstration from parents, because they see that their student knows the material, but is confused as to why they seem lazy, confused, or uninvolved. Break this habit by asking them leading questions. These are questions that will guide the student back to their work and will also force their brain to do the thinking. Here are some example leading questions:

1. What is the first/next step?

2. What do you think you should do next?

3. Why did you do it that way?

4. What is the question looking for?

5. What information from the problem is given?

6. Do you notice a pattern?

These questions and many more are only helpful if you do not answer them for your student. This will train them to wait until you are willing to give the answer. Kids hate silence and when they realize you won't answer the question for them, their brain will start thinking. Blank stares often don't mean a lack of understanding, but a lack of thinking.

Singapore uses three methods of displaying numbers which helps students master mathmatics; concrete, pictoral, and abstract.

Concrete

Students will use concrete objects to visually see and physically manipulate things that are representing numbers. These may include; counting bears, counting squares, place-value discs, fraction tiles, or even pieces of paper.

This way of working with numbers shows students that numbers mean things in the real world and are not relegated to the classroom. This can also be a fun experiement for them as they attempt to make sense of the world of numbers using real objects. 

Pictoral

Once students have a feel for numbers and the way that they work in the real world, they move on to visually representing numbers with pictures. At first, this takes the form of counting apples, moves onto grouping colored dots, and eventually the dreaded bar model.

The bar model's purpose is to stand in as a representative for the numbers, providing a visual framework for what the student is to be doing with the problem. Although they only seem to add to the already overwhelming confusion and stress that math sometimes brings, they truly are far more helpful than you would imagine.

Abstract

This is often what parents mean when they say that this is the math they learned. Abstract refers to the actual numbers, equations and other things often associated with math. This however, is not the best way to introduce students to mathmatical concepts. Their brains have not yet developed the ability to think abstractly about much of anything. Things that cannot be seen or touched, are often very confusing things for students to understand. Think of explaining timezones to a kid and how the time in England is different from the time in Denver. They will immediately believe that timetravel is possible because their time is different. Instead, students are introduced to mathmatical concepts with concrete items so that they can touch and move items to prove to their brain these mathmatical truthes.

Although seemingly complex bar models are quite simple and have a set of steps which can help students in their quests to solve them. Just remember RAWMEAT which stands for:

• Read

• Analyze

• Write

• Model

• Evaluate

• Answer

• Test

Although this is a silly acronym that is probably more complex than it needs to be (because Mr. Tomlin thought it was funny) it can be incredibly helpful.

Read: Although you would think that this is an easy step that none would skip, many students don't even try to read the problem before asking for help. So, have the student read the problem to you out loud. Then have them reread it. Silly, but sometimes it helps us check for any question we may not be understanding.

E.X. Orchard A has half as many trees as Orchard B. Orchard B has 4 times as many trees as Orchard C. Orchard C has 632 trees. How many trees in total do they all have?

Analyze: If your student only read the problem once, they will need to do it again in this step. Have them underline any information that is important for understanding the problem. For some students, I will even have them strikethrough anything that is unimportant, distracting, or not helpful. I will also circle or highlight what I am looking for in the question. Sometimes, pulling the information away from the paragraph can help alleviate the stress of reading and doing math.

E.X. Orchard A has half as many trees as Orchard B. Orchard B has 4 times as many trees as Orchard C. Orchard C has 632 trees. How many trees in total do they all have?

Orchard A: 1/2 of Orchard B

Orchard B: 4 x 632 (Orchard C)

Orchard C: 632 Trees

Write: Students will then write an answer sentence that is responding to the question that they are being asked. Not only will this show that they know what is being asked of them, it also helps keep their mind focused on the goal. This should be a complete sentence with correct spelling, punctuation, and grammar.

E.X. Orchard A has half as many trees as Orchard B. Orchard B has 4 times as many trees as Orchard C. Orchard C has 632 trees. How many trees in total do they all have?

Orchard A: 1/2 of Orchard B

Orchard B: 4 x 632 (Orchard C)

Orchard C: 632 Trees

Answer Sentence: There are ____________ trees in total.

Model: Now comes the part that seems hard, but is usually quite simple. I like to start by finding the section that I already know and drawing the model based on that one. Each section of the bar is called a unit and is a pictoral representation of a number.

E.X. Orchard A has half as many trees as Orchard B. Orchard B has 4 times as many trees as Orchard C. Orchard C has 632 trees. How many trees in total do they all have?

Orchard A: 1/2 of Orchard B

Orchard B: 4 x 632 (Orchard C)

Orchard C: 632 Trees

Answer Sentence: There are ____________ trees in total.

(Photos of bar models are on the photo carousel below this drop down menu)

Evaluate: Here, students will need to find the totals of each group and make sure that they properly calculate what is being asked of them.

E.X. Orchard A has half as many trees as Orchard B. Orchard B has 4 times as many trees as Orchard C. Orchard C has 632 trees. How many trees in total do they all have?

Orchard A: 1/2 of Orchard B

Orchard B: 4 x 632 (Orchard C)

Orchard C: 632 Trees

Answer Sentence: There are ____________ trees in total.

(Pictures of the bar models for this problem are on the photo carousel below this dropdown menu)

In total, there are seven units between all of the Orchards (Orchard A has two, Orchard B has four and Orchard C has one) Therefore, multiplying 632 by 4 will get me my answer.

632 X 4 = 4,424

Answer: Students will fill in their answer problem with the answer they discovered during this section.

E.X. Orchard A has half as many trees as Orchard B. Orchard B has 4 times as many trees as Orchard C. Orchard C has 632 trees. How many trees in total do they all have?

Orchard A: 1/2 of Orchard B

Orchard B: 4 x 632 (Orchard C)

Orchard C: 632 Trees

Answer Sentence: There are 4,424 trees in total.

(Pictures of the bar models for this problem are on the photo carousel below this dropdown menu)

In total, there are seven units between all of the Orchards (Orchard A has two, Orchard B has four and Orchard C has one) Therefore, multiplying 632 by 4 will get me my answer.

632 X 4 = 4,424

Test: This is where students will check to make sure their answer is correct. This is usually a simple math problem to show whether or not their answer makes any sense.