# Investigations Blog

## Q&A: The Definition of a Trapezoid

Question: Why did you decide to use the exclusive definition of a trapezoid? As the question suggests, there is more than one definition of a trapezoid. Mathematicians define trapezoids in one of two ways: Using the inclusive definition, all parallelograms (which include rectangles, squares, and rhombuses) are trapezoids. Using the exclusive definition, they are not. In determining which definition to use, we thought about a couple of things: Most elementary textbooks use the exclusive...

read more## A Grade 3 Q&A: Assessing the Multiplication Facts

Question: Why do the assessments of the multiplication facts in Grade 3 include a time limit? In Investigations, the overwhelming majority of students’ work with the facts is focused on making meaning of the operation of multiplication, building connections between problems and images that represent them (e.g. problems about things that come groups, arrays), and using what they know to solve what they don’t (e.g. how can knowing that 3×4=12 help with 6×4?). This work happens in...

read more## A Grade 3 Q&A: Why start with multiplication and division?

Question: Why does 3rd grade start with a multiplication/division unit and not addition/subtraction? Answer: We often hear from people who wonder why Grade 3 starts with a multiplication and division unit—just like it did in the 1st edition!—rather than an addition and subtraction unit. As we decided on the sequence of the units in any grade, we considered many different things. The most important was the development of mathematical content within and across grades. In Investigations 3,...

read more## A Kindergarten Q&A: Numbers Represent Quantities

As we said in the original post, our ideas for our blog are wide-ranging. We are excited to have a space that offers us the opportunity to answer common questions from the field. This Q&A is the first of that type of blog post. Have questions you’d like to see answered? Email us. Question: How do Kindergarteners learn to write the numbers, and use them to represent quantities? Answer: We are frequently asked about how Investigations supports young students in the development of numeral...

read more