Gathering Base Line Information
Ongoing assessment is one of the key principles in understanding your students’ mathematical thinking. To make learning meaningful, you must first have a thorough understanding of your students’ prior knowledge.
Below you will find a series of free online math assessments which can be used in the classroom. These problems use basic subtraction (also referred to as “separating from”) concepts. The word problems in this series are classified according to the standards set forth by the Cognitively Guided Instruction approach and progress through an identified continuum of knowledge development as detailed in the findings of Fennema, Carpenter, et al., and can be used as math teaching assessment tools to give you a better understanding of where each student falls on that continuum.
Please refer back to earlier articles in the series to understand what the notations mean after each problem.
1. Mr. Seghers (our Principal) has 8 pencils. He gives 3 pencils out as birthday gifts. How many pencils does Mr. Seghers have left? (Separate - Result Unknown 1)
2. Our teacher, Mrs. Wistrom has 23 cookies. She gives 6 cookies to Mrs. Zarling, the school nurse. How many cookies does Mrs. Wistrom have left? (Separate - Result Unknown 2)
3. Tommy has 62 marbles. He gives 22 marbles to Dan. How many marbles does Tommy have left? (Separate - Result Unknown 3, without regrouping)
4. There were 51 fish swimming by the pier. 28 fish swam away. How many fish were left swimming by the pier? (Separate - Result Unknown 4, with regrouping)
Solution Strategies and a Sample Problem
Here is a sample problem:
Colleen had 10 goldfish. She gave 3 goldfish to her friend, Mary. How many goldfish does Colleen have left?
Children’s solution strategies evolve over time. There are two main solution strategies that children employ when solving separating problems - Separating From and Counting Down. At the most basic level, they use physical objects (like counters or their fingers) to directly model the action in the problem. This would be “Separating From.” In the problem above, this would equate to the student taking the larger number (10 goldfish) in the problem and will remove the smaller number in the problem (3 goldfish) from the set. They will then count the number of objects (or fingers) remaining to find the answer.
A more advanced solution strategy would be a counting strategy known as “Counting Down.” To demonstrate the action in the problem, the student would use a backward counting sequence. He/she starts counting at the larger number from the problem and counts backwards.
Other Problem Types
The free online math assessments to be found at Bright Hub are not limited to addition problems. For problems involving addition, multiplication, division or more advanced mathematical concepts, please refer to the other articles in this series.
This post is part of the series: Math Assessment Test - Creating Baseline Data to Guide Instruction
This series of articles will give specific problems which can be used to create a math assessment test for addition, subtraction, multiplication and division concepts. The math assessment test results can then be used to guide instruction for students on an individual basis.