Here is a Jamboard to introduce volume and units of volume. (See photo at very bottom for making a copy to edit.)

The students start with building an animal pen and shading in the space inside. The hands on approach and connection to prior knowledge of a fenced in area for animals sets the stage for actual measurement units in subsequent slides.

The photos below show how students will count out meters and square meters, adding a formal layer to the fence they built previously.

The following slide provides an entry point to understanding volume and units for volume. The students count out cubes, building on the counting of meters and square meters. The cubes were created using WORD Paint 3D. Here is an article I used to create these. For the grid that is tilted, I used functions on WORD – see this document. (I could have used Paint again.) I then show them the prism that is created but I am not discussing shapes yet to keep the focus on the concept of volume.

I then have students recreate the volume using NCTM’s Illuminations activity called Cubes.

Finally, I show examples of volume and move from cubic units to liters (litres – as I was initially teaching this lesson to a 5th grade class in India).

The fractional units of a ruler and measuring fractional lengths can be tricky, especially for students with processing, working memory, or visual related disabilities. For the students I have helped, here is the approach I have used.

I relate the fractional marks and counting them to walking across a set of stepping stones. This ties into their prior knowledge and allows for a hands on activity of moving the girl across the stones.

I present the girl and the stepping stones as the setting. Then I explain that she will take steps to walk across the stepping stones to the other side. Students count stones to determine steps. Below is an image of a Jamboard that allows for moving the girl.

Below is an image of a handout I use to address this prior knoweldge.

To help students learn how to measure with a ruler, I focus on minimizing the number of tic marks on the ruler at first. The image below shows an excerpt from a WORD document with a halves ruler that I use and an instructional strategy. It also contains a quarters and an eighths ruler that students can slide around the WORD document as shown above and in a video explaining this artifact and how I created it.

This is useful for distance learning as well as in class. Here is a link to the WORD document with the rulers shown in the video.

Math is often considered an esoteric set of information that is disjointed from the reality people face, aside perhaps from money. Sadly, in school, especially in older grade levels, math is indeed presented this way.

A situation as simple as riding an elevator provides opportunities to show and engage a student with math applied in authentic and common situations. For example, the elevator buttons address counting and cardinality (4 indicates a total of 4 floors – ignoring the R), comparison (if we are on floor 2 and need to go down, which floor do we go to?) and measurement (height above ground floor measured in floors). Such situations also provides opportunities for generalization into other settings – the important settings of every day life!

The photos below are used to introduce length and area as part of a CRA approach. First a student is asked to build a Lego garage. He first builds the bottom row of a wall and the teacher asks for length in terms of how many Legos are lined up. After building a wall the teacher asks for area in terms of how many Legos are used in the wall. Then the student is given a handout with the following photos. Following this handout the student finds length and area of tiled floor and walls made up of cinder blocks, if available. Eventually a ruler is introduced and multiplying to find area is presented at the end.

For the photo above the student is asked to count Legos to compute length. In the photo below the student is asked which is longer and to explain.

In the photo above the student is first asked to determine the area of the red wall in terms of number of Lego squares. Then the student is asked which wall has more area. This is followed by the photo below. This allows a different perspective of area.