Oakland Terrace Grade 4 Math

Ms. Gale's class explored equations with parentheses and multiplying three factors first with concrete objects. This student made an array with linker cubes showing (6 x 2). Because she multiplied (6 x 2) by 5, she had to make 5 arrays in all. She made the rectangular prism drawn here first with linker cubes. The concrete prism and the drawing on the left show that (6 x 2) x 5 = 60. It also shows that no matter where the parentheses are placed, the product will be 60. If the expression were written (6 x 5) x 2, she would have first made the bottom row (6 by 5). She then would double the number of rows because she multiplied by 2. The product of (6 x 5) x 2 is still 60.

Indicators
1.4.2.1 write numeric expressions in equivalent forms using the commutative and associative properties.

6.4.6.1 simplify numeric expressions involving parentheses.

The isometric dot paper used here makes drawing three dimensional objects much easier. Some students will have an easy time seeing how to draw prisms on the paper; others will struggle. If students orient the solid facing them the way it looks in the above drawing, (with one edge pointing toward them) it makes drawing easier. Also, point out to students that they are only drawing the edges and faces they can actually see. Pair students or place them in groups of three so they are more successful. Also, try drawing yourself before you expect the students to do it. Sometimes, adults struggle more than the students.

These students drew much simpler prisms. The parentheses could now be introduced. The equation below could be written as (2 x 6) x 2 = 24, or even as (2 x 2) x 6 = 24. On the right, the equations could be written as (2 x 3) x 2 or (2 x 2) x 3 = 12. It makes sense to start with easier numbers like the ones to the right, and then have students move to equations like the one above.
Grade 4 Unit 2

This is work from Ms. Flory's class.
Grade 4 Unit 2

$Download Isometric Dot Paper$

Download Isometric Dot Paper

$Download Isometric Dot Paper$

Online Isometric Geoboard

$Online Space Blocks$

Online Space Blocks