MathJewels math guide · Count and compare within 20
Counting, Comparing, and Making Small Numbers
Build early number sense by matching one count word to each object, recognizing the total, comparing collections, and composing a number from smaller parts.
The big idea
Counting connects each object to exactly one count word. The last word said tells how many objects are in the whole collection, even if the objects are rearranged. Comparing asks which collection has more, fewer, or the same number. Composing and decomposing ask how one total can be made from smaller parts.
These ideas are related: a child must trust the total before comparing it or breaking it apart.
Worked example
A jar shows 3 fireflies and needs 5 altogether. Count the visible collection: 1, 2, 3. Continue counting while adding objects: 4, 5. Two objects were added, so 3 + 2 = 5.
The total 5 can also be split as 4 and 1, or 2 and 3. The arrangements differ while the total stays 5.
How children may show it
Children may touch or move each object while counting, match two collections object by object, use fingers or a five-frame, draw missing objects, or write an addition equation. Rearranging a counted collection is a useful check that spacing does not change how many objects exist.
Common mix-up
A child may skip an object, count one twice, or believe a spread-out row contains more than a close row. Encourage one-to-one matching or physically move each counted object. When finding a missing part, make sure the original objects remain visible and only the new objects are counted as added.
Try it together
Make a collection of 5 small objects and hide some under a cup. Show the remaining objects and ask how many are hidden. Reveal and count to check. Repeat with different splits, then ask which visible collection has more without changing the total of 5.