Illustrative Mathematics Grade 5, Unit 1: Finding Volume
In this unit, your child opens the year with volume. They build and count unit cubes to see what it means to fill a space, then find the volume of rectangular prisms by multiplying length, width, and height, or base area by height. They also find the volume of figures made of two prisms. Next comes a unit on fractions as quotients and fraction multiplication.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
What is my child learning in Unit 1?
- Building with unit cubes to see that volume is the space a solid fills, with no gaps or overlaps. Learn more: Volume: how much space is inside a solid
- Counting cubes in layers to find volume, and measuring in cubic centimeters, cubic inches, and cubic feet. Learn more: Finding volume by counting cubes
- Finding the volume of rectangular prisms with length × width × height or base area × height, and of figures made of two prisms. Learn more: Finding the volume of a box
Sample questions to try together
These are real questions from our practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
Hana stacks 12 unit cubes into a tall tower. Then she takes it apart and uses all 12 cubes to build a long, low wall. How does the volume of the wall compare with the volume of the tower?
- They have the same volume
- The tower has more volume
- The wall has more volume
How you can help
- Use blocks or sugar cubes to build a box 4 long, 3 wide, and 2 tall with your child. Ask how many cubes it takes before counting, 24.
- Guess which of two kitchen containers holds more, a tall narrow one or a short wide one. Then fill one with water or rice and pour it into the other to check.
- Measure a drawer or laundry basket with your child and multiply length × width × height. Ask what the answer, in cubic inches, actually counts.
Where kids can get stuck
- Assuming the taller container always holds more, when a short, wide box can hold more.
- Ignoring gaps and overlaps, estimating volume by tossing cubes loosely into a box and counting them.
- Adding the three dimensions, so a 4 by 3 by 2 prism gets 9 instead of 24.
Practice makes perfect
Bobby's Math Club has practice problems that adapt to your child’s level, each with a detailed explanation and an easy-to-follow video, so your child can build confidence in these skills one step at a time.
Words your child will hear
- volume
- How much space a 3-D shape takes up or holds.
- unit cube
- A small cube that counts as 1 cubic unit.
- cubic unit
- A cube with sides 1 unit long, used to measure volume.
- rectangular prism
- A box shape with six rectangle faces.
- layer
- One flat level of cubes in a box; stacking layers fills the box.
- base
- The bottom face of a solid, whose area times the height gives volume.
- height
- How tall a solid is, from its base to its top.
- solid figure
- A three-dimensional shape, like a box or a cube.
Ready to build your child’s confidence with measuring volume?
In Bobby's Math Club, your child practices these skills at just the right level, with a hint when they need one, a clear explanation after every question, and kid-friendly videos. Unlimited practice is free.
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Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
Which math standards does Illustrative Mathematics Grade 5 Unit 1 cover?
Illustrative Mathematics Grade 5 Unit 1 covers these math standards. Each one links to what it means, sample questions, and teaching strategies.
For teachers: Unit names and order vary between editions and districts, so your school’s own materials have the exact sequence. Learn how Bobby's Math Club can help your students grow.