Our Learning (Math)

Primary Check List

  Using the place value dice, we create a number. Then we use the list to investigate our number.

Being Familiar With Numbers

Using place value dice, we looked at the digits of a 3-digit number. We rearranged the digits to make other numbers. We call these permutations.

Inequality and Equality: Greater than (>), Less Than (<), Equal to (=) 

These mathematical signs were recently introduced.  As we read left to right, it is important that we read mathematical equations from left to right as well.  We are used to reading mathematical equations with the “=” sign (“equals”), where both sides of the equation is balanced.  With “>” and “<“, these mathematical symbols have a meaning as well when we are describing a relationship between two numbers.      

“>” is the symbol for “greater than” and “<” is the symbol for “less than”    

Examples:    

15 > 11       15 is greater than 11                78 > 52      78 is greater than 52    

24 < 39      24 is less than 39                    12 < 20      12 is less than 20  

Understanding Place Value

Understanding numbers requires us to break down the components of the number. By looking at each component (ones, tens, hundreds), it helps us to understand how many ones, how many tens, and how many hundreds are in each number. As they grow older, the numbers they will work with will get bigger, but the idea stays the same. Standard notation is how we normally write the numbers but expanding the components (‘expanded notation’) helps us to see how many ones, tens, hundreds, etc. are in the number. We are now playing games using place value dice. 

Palindrome

A palindrome is a word or number that is the same whether we read it from left to right or right to left.

100 Day – Feb. 20, 2024

  Which “groups of” make exact groups to 100? We learned that groups of 2, groups of 4, groups of 5, and groups of 10 all make exact groups to 100.

Patterns

We briefly talked about patterns and how patterns have a part that repeats. On a repeating pattern, the core repeats over and over. For a growth pattern, something repeats. On the groups of 2s pattern, the ones place value (2, 4, 6, 8, 0) repeats over and over again.

Number Riddle – Strengthening our number skills

We have been strengthening our number sense by doing number riddles. We use our place value pockets and digit cards to figure out the number. By using the place value pockets with the digit cards, we can switch up the digits chosen with each clue until we get to the correct number. This picture is an example of a number riddle we did. The more comfortable and understanding the students have in deciphering the clues will help in strengthening their math skills. 

Week of Jan. 31-Feb. 2

Mar. 4

Apr. 8 and April 10

Number of the Day

Jan. 23 was the day where we have been coming to school for 82 days. Taking what we have been learning so far, we looked at the number 82. Here is what we know.

Feb. 2

Apr. 11

Place Value – Crux of Understanding Numbers

Our number system is called a ‘base 10’ system. There are ten digits from 0 to 9, which are numerical symbols we use to represent numbers in math. These digits are special because they are also numbers (single digit numbers). Numbers are when digits are placed to represent numbers which is similar to letters being placed together to form words. For example, 12 is a two-digit number and 1456 is a four-digit number. Digits are like letters and numbers are like words. Using digits together creates numbers in a similar manner to letters creating words. 

Looking closely at place value, when we read a number, we read from left to right but when we look at a number more closely, we look at the digits of the number from right to left as we look specifically at the ones, then tens, then hundreds, and so on.

‘Place Value’ is defined as, “every digit has a place, and every place has a value”. Starting from the right and going left, you have the “ones”, then “tens”, “hundreds” and so on. These are the place value pockets and the digits. Please notice how only one digit can fit in each pocket. 

Understanding Money

During the week of Jan. 8, we talked about the value of the money (coins and bills) and began to see equivalent amounts using coins, or coins and bills. We used school money (play money) to build our understanding.

A Visit from Ms. Tuan

As part of our learning of financial literacy, we had a visit from Ms. Tuan who is the Youth Credit Union Coordinator. She taught us about the importance of saving money and we made a bank. There is a Vancity day every Wednesday where students who have a Vancity membership can make deposits at our school.

Financial Literacy

During the week of Dec. 11, we began learning about money. We learned that before money was used, they used to trade things. However, to standardize and make standard unit of measure, money began to be used to buy things. It is essentially “trading” money for an item. We also talked about how each country has their own money with their own values. We looked at the coins we use and what they look like. We also looked at the value of each coin and their symbolic images on the back. We also looked at the ‘paper money’ and how it has changed over time. We also talked about the figureheads on each bill.

We also talked about how the money that we earn working has to be spent on “needs” and “wants”. We talked about how needs are things that are necessary for survival and wants are the extra things we can buy with whatever is left over.

Problem Solving

We are trying to strengthen our addition skills by incorporating everything we have learned about adding together with our listening and comprehension skills.

More Fact Families/Related Facts

When I ask the students what they can tell me about Fact Families/Related Facts, they tell me that the numbers live in a triangle house and have four equations (two plus equations, two minus equations). The smaller numbers live at the bottom of the triangle house and the biggest number lives at the top of the triangle. In the equations, the smaller numbers “like to switch places”. In the addition equations, the biggest number comes at  the end in the subtraction equations, the biggest number starts. The smaller numbers like to switch places. We now are looking at the triangles where there can be three placements of number. If the top number is missing, then we begin with the + equations. However, if one of the smaller numbers are missing, we begin with the minus equations. 

We also are now using fact families/related facts flashcards. Reminder that these are known as “the basic facts” as we go higher up the grades.

Fact Families/Related Facts – A Different Notation

Cross out to 18

This is a game where they roll the double decahedron dice and add the two numbers or subtract the two numbers trying to cross as many of the numbers (1 to 18) out as possible. If you roll a 9 and a 2, you can either do 9 + 2 =11 or you can do 9 -2 =7. 

Patterns

Counting in groups of 2, groups of 5, and groups of 10 on our number line is known as a “growth pattern” as the numbers are getting higher/getting bigger.

Repeating patterns on the other hand have a strand that repeats over and over again.

Related Facts/Fact Families

During the week of November 6, we began investigating Fact Families/Related Facts using the “pairs of numbers for basic facts”. The idea behind Fact Families/Related Facts is that three numbers are always connected/related to one another. This concept helps with strengthening their basic math skills which will continue to be useful in higher grades. For example, 2, 3, 5 are related to each other because if you add 2 and 3, the answer will always be 5.  Rather than memorizing a bunch of random mathematical equations, retention will occur if we are able to connect numbers together.  To help with relating the three numbers, we use a triangle as the symbol.  The two smaller numbers (which will be the addends) are at the base of the triangle, and the sum is at the top of the triangle (the biggest number).     

When I ask the students what they can tell me about Fact Families/Related Facts, they tell me that the numbers live in a triangle house and have four equations (two plus equations, two minus equations). The smaller numbers live at the bottom of the triangle house and the biggest number lives at the top of the triangle. In the equations, the smaller numbers “like to switch places”. In the addition equations, the biggest number comes at  the end in the subtraction equations, the biggest number starts. The smaller numbers like to switch places. Here is an example of the work.    

Please note that this incorporates Commutative Property and Odd/Even Property. This is also an important concept for learning our basic facts to 18, which is something we will use going forward in every grade, and for the rest of our lives.  

Addition and Subtraction

During the week of Nov. 6, we began looking at subtraction. To help solidify this concept, the students were introduced to its other names, “minus”, “take away”, and “subtract”.  Mathematicians call these subtraction or difference equations.  We looked at these two math operations as being opposites to one another. It is important to understand the basic concepts of adding and subtracting as these building blocks for more complex math concepts. 

Commutative Property

The property is “a + b = b + a“.  This means that any number plus a second number is equal to the second number plus the first number.  An example is 3 + 4 = 4 + 3.  OR “a + b = c and b + a =c”. This means that any number (a) plus another number (b) is equal to a completely different number (c) that is not the same as the first and second number. These are called ‘algebraic symbols’ and represent a rule that remains for any numbers that can be put into a, b, or c. This may seem trivial but learning this property will help students in understanding relationships between numbers as they progress further in their learning. 

Odd/Even Property    

During the week of Oct. 16, we explored our study of mathematics a little deeper. A characteristic a number has is that they are either odd or even. Numbers are either odd or even, and do not flip flop back in forth depending on the day. That’s what makes mathematics more predictable, unlike all the rules to the exception in the English language. We began our conversation by looking at each individual from one to thirty and decided whether everyone in the number had a partner or not. Then we lumped all the numbers without the partners in one group and lumped all the numbers who all had partners in another group. We discovered that all the numbers whose last digit (ones digit or place value) ended in 1, 3, 5, 7, or 9 were in one group, and all the numbers whose last digit (ones digit or place value) ended in 2, 4, 6, 8, or 0 belonged to another group. The mathematical definition are as follows:      

-An odd number is any number whose ones digit is 1, 3, 5, 7, or 9    

-An even number is any number whose ones digit is 2, 4, 6, 8, or 0 

During the week of Oct. 23, we learned about the Odd/Even Property, or rule. Knowing this helps to anticipate what kind of answer we should get. This is what we learned this week.

Learning Pairs of Numbers

Math is all about relationships between numbers. Finding the patterns of  pairs of numbers helps to create familiarity and predictability in mathematics. We looked at all the single digit pairs of numbers of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18. This is what they learned. These are what is known as the “basic facts” and is something that is used throughout our lives. 

We are learning the pairs of numbers that go together to help with our basic facts.

How we got the pairs for 5.

Dominos (two dice together) 

Dominos are like two dice stuck together. We play a game where all the dominos start upside down. We pick up each domino and add the dots as quickly as possible. We then put it on the bananas with the corresponding number. This is a different way of adding two dice together.  

We are beginning to see pairs of pips for a number for example, two pips and four pips are six pips, but three pips and three pips also make 6 (2, 4, 6; 3,3,6). We recognized that the number six (6) had the greatest number of pairs.

Adding

Since we have been playing with two dice, we are essentially adding all of the dots together. For this reason, we talked about what the concept of ‘adding’ is. Here is what they said.

Number Formation:   

As with printing proper letters, printing numbers is also an important skill. The concept of reading and writing left to right, up to down helps to build fluent readers. To help them learn how to print the proper numeral formation, I have taught them a rhyme to help them.  We have practiced them using our whole body, writing with our fingertips, and finally printing them on lined sheets. We have talked about digits being the same size as upper case letters so they are “tall”. 

• Down and around, that’s my hero makes the number zero (0)(the numeral 0 is an oval shape and the letter is a round circle)   
• A line down from the sun, makes the number one (1)  
• Around and back choo choo, makes the number two (2)  
• Around the tree, around the tree makes the number three (3)  
• Down and across and down once more, makes the number four (4)
• Down and around and back for a drive, makes the number five (5)
• Like a monkey doing tricks, makes the number six (6)
• Straight across and down from heaven, makes the number seven (7) 

Subitize:    

As humans, it is difficult to look at a bunch of things and be able to recognize more than five or six things at a glance without having to physically count each thing.  Therefore, being able to subitize, looking at a quantity of things and know how many there are without physically counting out each thing, is an important skill to have.  For example, if we roll a die, there are between one and six dots on each of its sides.  If we were to roll a six, it is easily recognizable without having to count each dot.  As an adult, this is a skill that we have built up over time.  Teaching children the skill to subitize is important so that they are able to count on and not always start back at one to find out how many there are.  

Shapes:   

As part of their math tool bag, each student has a bag of pattern blocks. The students can play with the pattern blocks as part of their morning activity or when they have free-time. I believe that using the correct mathematical terminology is important so I have taught them the names of the shapes.  Each student has a bag of pattern blocks containing a variety of shapes with specified quantities that they count before and after playing with them. The picture below is the legend they use to ensure that they have all the pieces.