# Investigations Blog

## A Grade 2 Q&A: The Size of the Numbers

Question: If the CCSS indicates that Grade 2 students are supposed to be working with numbers to 1,000, why doesn’t this work begin sooner? Why are students still working with numbers under 20 and numbers under 100 for so much of the year? Answer: The Common Core State Standards at Grade 2 include work with numbers up to 1,000, but it is important to look closely at what students are expected to do with these numbers. In Grade 2 students are developing efficient and accurate strategies...

read more## Q&A: The Order of the Units

Question: Can the Investigations units be taught in a different order than suggested? Answer: The first edition of Investigations was written as a “replacement unit” model where individual units within a grade were somewhat less dependent on previous units, and schools and districts often chose their own sequence, or decided to teach only 3 or 4 units the first year of implementation. That was the 1990s! The units in the 2nd and 3rd editions were written as a complete, coherent, full-year...

read more## Q&A: Mathematical Vocabulary in Investigations 3

Question: How does Investigations approach the teaching and learning of mathematical vocabulary? Answer: In Investigations 3, mathematical vocabulary is introduced as a natural part of the conversation during activities and discussions, along-side students’ own words. Rather than memorizing the definitions of new terms, students come to understand such words as factor or area or symmetry as they investigate and discuss new concepts. Hearing new mathematical terms used regularly, and having...

read more## Q&A: The Definition of a Trapezoid

Question: Why did you decide to use the exclusive definition of a trapezoid? Answer: 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## Q&A: Quizzes in Investigations 3

Question: The Quizzes in Investigations 3 are new to us. We are used to assessing the benchmarks with the Meeting/Partially Meeting/Not Meeting system outlined in the Assessment Teacher Notes. Can you help us get a better sense of how to use the Quizzes as they relate to the Unit’s benchmarks? Answer: Quizzes are included in grades 1-5 of Investigations 3, to give students experience with next-generation test formats, such as: multiple choice fill-in-the-blank questions with more than one...

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? Answer: 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 3x4=12 help with 6x4?). 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...

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