Practice
10. Try better practice.
Let's commit to being purposeful about students' practice within this standard. If a student can correctly solve three to five 2 x 2 digit multiplication problems, there's no reason to have them continue to solve seven more of the same thing. Piling on tons of problems could lead to unnecessary frustration and an increased chance of cementing a misconception if it's not caught early. Instead we want to offer practice opportunities that allow students to go deeper with their understanding by providing tasks with a "high ceiling". Below are a few better ways to practice that you might choose to add to your tool belt.
Open Middle Problems
From the Open Middle website: "Open Middle problems have...
a “closed beginning” meaning that they all start with the same initial problem.
a “closed end” meaning that they all end with the same answer.
an “open middle” meaning that there are multiple ways to approach and ultimately solve the problem.
Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding."
Many open middle problems use digits 1-9, each no more than one time, to meet a given criteria. These problems often uncover student misconceptions and/or lead to students drawing generalizations.
All current Open Middle problems from the website have been added to Google Slides templates by Dan Shuster and can be found here. You may also be interested in the Open Middle book which offers much more detail about effective use of this type of problem in the classroom.
Error Analysis
How many times have you asked a student to go back and check their work to find a mistake, only to watch them melt down? Finding mistakes is a skill we need to practice. There are multiple error analysis routines we can use in the math classroom such as Find the Flub, My Favorite No, or Two Truths and Lie.
Would You Rather?
This is a simple routine that can add in problem solving, reasoning, and communication skills to students' computational practice. They are presented with two similar situations and need to justify which one they would choose using mathematical reasoning. Check out the website Would You Rather Math for inspiration.
Frayer Model
The Frayer Model is a graphic organizer typically used for building understanding of new vocabulary. There are many ways to used this tool in math, but for standard 5.4 you might consider putting an expression like 35 x 42 in the center and asking students to fill in the following in the remaining four boxes:
A practical problem that would be solved with this expression
Show how you use rounding to estimate
Model the problem
Solve using a method of your choice, and compare to the estimate
