understanding 2-digit numbers

First grade isn’t the first time that your students have been introduced to the idea of 2 digit place value!

In kindergarten, students get their first taste of place value as they count by 10 and as they build teen numbers. This is only the foundation as kindergarten students are largely working with individual units and rote memorization.

In first grade, the task is to UNDERSTAND two-digit numbers. This can be done by building with hands-on materials, drawing place value drawings and discussing two-digit numbers in terms of tens and ones, and showing this thinking on a place value chart.

The 5 examples listed are certainly not an exhaustive list of tools and lessons that could be used to teach this skill.

They are rather a sample progression from hands-on to abstract thinking!

Which step represents your students’ current level of understanding?

Your students likely have rote skills when it comes to decade numbers. Bringing meaning ot this rote counting is the first step in understanding 2 digit place value!

Consider using a tool like linking cubes with a sticker on each cube. Write the numbers 1-100 on the cubes as your students count aloud.

As you count, group the cubes into stacks of ten. What do your students notice about the number at the top of each stack? They are the decade numbers!

Explore with your stacks of ten cubes. How many cubes do we have if we have 4 stacks or towers of cubes? How do we know?

Linking cubes are a groupable model. This means your students can physically group 10 ones together to create a ten-stick.

This is where you want to start in terms of hands-on tools for building 2-digit numbers.

Provide a context for your students, such as I have 5 packs of markers with 10 markers inside. I also have 3 extra markers. Ask your students if they can use linking cubes to build a model that matches the story.

Can they figure out how many markers there are in all?

Honor the fact that your students’ instince may be to count each cube individually and gently prompt and question your students to encourage them to see the place value connections.

You want to be sure that your students understand 2 digit place value, not “how to build numbers with linking cubes”.

To prevent this common problem, introduce a new material and ask your students to draw connections between the work they did with linking cubes and a new material such as straws that can be bundled together.

Dump a large pile (40-60) straws onto the table and ask your students how many straws are in the pile. Some students will still tend towards counting by 1s but you will begin to see students bundling straws together to organize and more efficiently find the total.

Using these bundles, you can ask your students to build a variety of numbers from this material as well.

Alongside hands-on models such as linking cubes and bundles of straws, you can encourage your students to draw their own representations of 2-digit numbers by drawing sticks and circles.

Provide context for your students in their math drawings. A story such as “I am making bracelets for my friends! Each bracelet uses 10 beads. So far I have made 7 bracelets and a tiny ring that only uses 3 beads. How many beads have I used so far?”

Allow your students to build this story using their choice of math material but also ask your students to draw a place value drawing with sticks and circles that matches their model.

In previous lessons you have used story problems alongside your students 2 digit place value learning. Continuing to use these stories without hands-on or picture support demonstrates an understanding of 2-digit numbers at an abstract level.

A story such as “Marissa has 4 new ten-packs of markers and 6 more markers in her desk. How many markers does she have in all?” provides a context that supports place value thinking.

Ask your students how many markers they think Marissa might have without using any materials at all. Ask them to defend their thinking using place value thinking.

Step backward to drawings- could your students draw a place value drawing to match the context? Does their thinking change around how many markers Marissa might have or are they still feeling confident?

You can continue to step backward to hands-on materials as well to confirm your students’ thinking.