When planning for CGI instruction, starting with the standards can help to ensure students are ready for the academic challenges that lie ahead this year and in the years to come. Below is a 5 question format that can be used to align CGI lessons with the Common Core content standards.
1.) What is the standard(s) I want to specifically teach into?
2.) What CGI problem types align with this standard?
3.) What are the number choices I can select to support and nudge my students while they are grappling with new learning?
4.) What physical tools or models might they need to gain understanding and/or extend their thinking?
5.) What questions might I ask to help students make connections to new and big or small ideas?
First Grade:
Numbers and Operations in Base 10 – (NBT. #2 a, b, c.) Understand place value. – b. The numbers 11- 19 are composed of a ten and one, two, three…
Problem Type: Part-Part Whole (Addend Unknown) 5 = 3 + ___
Mrs. Moore has ___ pieces of paper. She spilled coffee on ___ of them. How many copies are still clean?
Number Choices: (15, 5) (23, 3) (37, 30) (40, 30)
Tools and Models: Base ten blocks, ten frames, money (coins and dollars)
Questions and Connections:
Do you have any groups of ten in your drawing? How many? Do you have any ones left over? How many?
What coins/bills could we use to help us solve this problem? Why?
What would this look like if we used ten frames to solve?
What would this look like if we used base ten blocks to solve?
These are some of the tools, models and questions I would use. What others could you try? What numbers might you use on day 2, 3?
Depending on how (models and strategies) students solve the problems, it could align with many more of the standards.
Third Grade
Standard: Numbers and Operations in Base Ten and Operations and Algebraic Thinking1, 2, 3, 5 (NBT #2, 3)
Problem Type: Join Result Unknown or Grouping /Multiplication
Mrs. Moore has ____ pieces of paper. She put ___ in each teachers’ mailbox. How many mailboxes did she fill?
Number Choices: (1,000, 100) (400, 10) (32, 4)
There are ___ pencils on every table. There are ___ tables. How many pencils are there?
Number Choices: (100, 10) (40, 10) (8, 4)
Tools and models: Number Line, array, ten frames, base ten blocks
Questions and Connections:
What do you notice about the number choices and answers you got in problems 1 and 2? How are they different? How are they similar?
What would this problem look like if we solved it using a number line? Where would you start? Where would you go next?
What numbers might you put in the boxes if you used a ten frame?
What would this problem look like if you used base ten blocks?
These are some of the tools, models and questions I would use. What others could you try? What numbers might you use on day 2, 3?
Fifth Grade:
Standard: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. # 3, #7
Problem Type: Measurement Division
Tim bought a ____ pound bag of dog food. Each serving is ____ of a pound. How many servings are in the bag?
Number Choices: (10, ¼) (12, 2/3) (7, 5/8)
Problem Type: Multiplication (Grouping)
The dog eats ____ of a cup of dog food ___ times per day. How much dog food is eaten a day?
Number Choices: (1 1/3, 3) (5/8, 4) (1 2/3, 4)a
Tools and Models: Drawings, area models, number lines, equations
Questions and Connections: What would this look like as a mathematical phrase? What academic language could you use to describe your steps or equations?
