December's Mathematical Focus 2019: Number Operations

School wide we using the professional text, The Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know (Erikson Institute Early Math Collaborative, 2014), to implement changes to instruction.  While we continue to have preschoolers work to sort, count, and deveolop number sense, we will be focused on number operations this month.  Look for some videos in your inbox and a handout in your child's Thursday/Friday folder this week.  

THIS MONTH’S BIG IDEA: Number Operations 

What are Number Operations? According to The Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know (Erikson Institute Early Math Collaborative, 2014), “…Everyday life brings up compelling questions about How many now? How many more or fewer? And is it fair? Number operations are the tools we use to find the answers to these questions.  When children focus on what happens when we join two sets together or separate a set into parts, they learn about how quantities change.  When they have lots of experience comparing amounts, they become familiar with thinking about differences between sets.  And when they have opportunities to see how a single large set can be composed of two or more smaller sets, they get comfortable with the fact that larger numbers contain smaller numbers (p.65).”

BIG IDEA #1 (Number Operations): Sets of objects can be changed by adding items (joining) or by taking some away (separating)

There are many every day scenarios that involve change—the adding to or taking away of some items within a set. 

COUNTING ALL: This strategy involves using objects to count all the objects, whether you have added some on or taken some away. First, count out the first set, then the second set, and then count them all together.

COUNTING ON: When we have a set of objects and add more—ask, “How many now?”


When practicing this, count on from the first number while keeping track of the counts.

BIG IDEA #2 (Number Operations): Sets of objects can be compared using the characteristic of numerosity, and ordered by more than, less than, and equal to.

We often talk about this concept at the dinner table.  If you have heard, “She has more than you!” at the table, your child is involved in comparisons. This will look like/sound like, “If Mommy’s plate has 5 carrots and Daddy’s plate has 8, how many more carrots does Daddy have?”

MATCHING: Line up two sets with one to one correspondence.

ORDER: Count both sets and determine which is more by thinking about which number comes later in the sequence of counting.

For example, if after reading a story about bunnies, we could ask children to prove their ideas by comparing sets using concrete items and lining them up. With this example, we can talk about how there are more red bunnies than yellow ones.  We can talk about how many there would be if we added them all together ( 3 + 5 = 8).  We can also discuss how many more yellow bunnies we would need to have the same amount of red and yellow bunnies (How many fewer?).  We can encourage to count up to find out.  We could also ask them how many more red bunnies than there are yellow and to show how they know. Which is more/fewer?  How many more/fewer?

BIG IDEA #3 (Number Operations): A quantity (whole) can be decomposed into equal or unequal parts; these parts can be composed to form the whole.

These scenarios involve a fixed number of items in a set.  In the everyday world, this might sound like (using concrete objects):

COUNT ALL – Composing numbers: Count out both parts and then count them all. For example,There are 5 slices of cheese pizza (1, 2, 3, 4, 5) and 5 slices of cheese and pepperoni pizza (1, 2, 3, 4, 5). 

COUNT ON – Composing numbers: Count on from the first number while keeping track of counts, for example, How many pizza slices are there in all? (5… 6, 7, 8, 9, 10 = 10 pizza slices)

COUNT ALL – Decomposing numbers: Count out the whole, count out a given part from the whole, and then count the remaining part.  For example, “We had ten pizza slices.  We ate three.  How many are left?”

COUNT ON – Decomposing numbers: Count up from the given part to the whole. For example, “We have 7 pieces of pizza left.  We already ate 3.  How many did we have before? (7 + 3 = 10)

Help us explore mathematics with our children in every day settings, scenarios, and life.  Children need repeated opportunities to explore and understand!

Source: Collaborative, Early Math. Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know. S.l.: Pearson, 2014.

With respect,

Paige Gordon, Principal

Tagged in Mathematics