CGI Math TLC Assessments of Math Understanding, by Linda Levi
CGI teachers find that it can be useful to have a record of students’ growth in problem solving throughout the school year that supplements their assessments students’ mathematical understanding during instruction. The problems included in these grade level assessments engage students with concepts that are particularly important. A student’s strategies for solving these problems will give you a window into that student’s understanding of these concepts.
Some teachers have shared student work from these assessments with parents. Some teachers show students their own assessments throughout the school year so that students can see their own growth.
Use these assessments in any way that works for you. Consider the following when using these problems with your students:
These problems were written as informal assessment for teachers to pose 2 – 4 times during the school year. They are not meant to replace formal assessments.
It’s intended that students solve the problems independently.
You are likely to get a more accurate understanding of children’s thinking if you divide this assessment and give it in two or more settings.
You may want to tell your students that this assessment is so that you can see how they grow over the year. They shouldn’t be worried about how their grade could be affected by how well they do on these problems.
You could choose to write notes on a student’s paper about what they observe while that student solves these problems.
The answer that the student provides is often not as important in understanding their thinking as the strategy that they used to solve the problem. Students might provide the same answer at the beginning and at the end of the year, but if their strategies are more sophisticated at the end of the year, you will know that their understanding of concepts embedded in the problem is deeper.
Grade levels are provided as suggestions. You could certainly pose problems from different grade levels if you wanted to.
Do what you can to ensure that reading or listening comprehension doesn’t impede any student’s ability to solve the problem. For example: read the problem aloud as many times as necessary. Change the context and the names in the problem to a context and names that your students are familiar with. Translate the problem into the student’s preferred language if you are able to.
The problems are written around generic contexts. Sometimes students, especially young students, will be better able to solve a problem if the context is interesting to them or something that they actually have done in the past. (For example, some children may be able to solve a problem about boxes of pencils and not be able to solve a problem about buckets of rocks if they have had experience putting pencils into boxes but don’t have experience putting rocks into buckets.)
It’s intended that students will have unit counters (grades K – 2) and base ten materials (grades 1 – 6) when solving these problems.
It’s intended that students will not have fraction manipulatives when solving these problems.
Students should have had discussions about representing their strategies on paper before they take this assessment.
It’s probably best not to have students complete this assessment for homework so that you can observe their strategies.
These assessments are intended to be used informally. Teachers have found these problems helpful in tracking student progress, having students reflect on their growth and sharing information with parents. These assessments have not undergone the rigorous analysis required for them to be used as standardized assessments or for them to be used to make a diagnosis of a child’s overall math achievement.
Kindergarten Assessment
1. Draw 7 dots on this paper.
2. Sasha had 7 cookies. She ate 2 cookies. How many cookies does Sasha have now?
More challenging numbers for later in the year, if needed: 12, 4 20, 5
3. I have 3 buckets with 2 rocks in each bucket. How many rocks do I have?
More challenging numbers for later in the year, if needed: 3, 5 3, 7
Kindergarten Assessment - Student Copy
First Grade
1. Sasha had 12 cookies. She ate 4 of them. How many cookies does Sasha have now?
Don’t change the numbers later in the year to see if students’ fact strategies get more sophisticated.
2. I have 3 buckets with 10 rocks in each bucket. How many rocks do I have?
More challenging numbers for later in the year, if needed: 6, 10 12, 10
3. Mario has 14 balloons. Lee has 8 balloons. How many more balloons does Mario have then Lee?
More challenging numbers for later in the year, if needed: 25, 17 60, 41
4. Our class had 40 pencils. We lost 21 of them. How many pencils do we have now?
You might wait until the middle of the year to pose this problem.
First Grade Assessment - Student Copy
Second Grade
1. Our class had 50 pencils. We lost 21 of them. How many pencils do we have now?
Don’t change the numbers during the year to see if students’ strategies get more sophisticated.
2. I have 39 books. How many more books would I need to get to have 42 books all together?
More accessible numbers, if needed: 19, 22
More challenging numbers for later in the year, if needed: 98, 103
3. I have 8 buckets with 10 rocks in each bucket. How many rocks do I have?
More challenging numbers for later in the year, if needed: 14, 10 32, 10
4. 61
- 59
Give the problem above in this form at the beginning, middle and end of the year. We aren’t expecting students to get the right answer in the beginning of the year. That’s ok.
5. 378 + 689 – 689 = n
Second Grade Assessment - Student Copy
Third Grade
1. I have 98 books. How many more books would I need to get to have 105 books all together?
2. I have 14 buckets with 10 rocks in each bucket. How many rocks do I have?
More challenging numbers for later in the year, if needed: 32, 10
3. Our class had 92 pencils. We lost 35 of them. How many pencils do we have now?
More challenging numbers for later in the year, if needed: 234, 68
4. 4 people want to share 5 cookies so that each person gets the same amount and there are no left overs. How much cookie should each person get?
Pay attention to how the student shows you their answer: with a picture; with words; with fraction symbols?
5. 61
- 59
Give the problem above in this form at the beginning of the year.
6. 301
- 298
Give the problem above in this form at the middle and end of the year.
7. 378 + 689 = 689 + n
Third Grade Assessment - Student Copy
Fourth Grade
1. I have 498 books. How many more books would I need to get to have 505 books all together?
More challenging numbers for later in the year, if needed: 2,995 3,015
2. I have 32 buckets with 10 rocks in each bucket. How many rocks do I have?
More accessible numbers for earlier in the year, if needed: 14, 10
More challenging numbers for later in the year, if needed 78, 10 335, 10
3. 4 people want to share 5 cookies so that each person gets the same amount and there are no left overs. How much cookie should each person get?
Give this problem at the beginning of the year. Pay attention to how the student shows you their answer: with a picture; with words; with fraction symbols?
More challenging numbers for later in the year: 4, 7
4. I have 3 large brownies. If I eat ¼ of a brownie each day, how many days will it take me to eat all 3 brownies?
More challenging numbers for later in the year, if needed: 6, ¾
5. 3001
- 2998
Give the problem above in this form at the beginning, middle and end of the year.
6. How many groups of ten are there in 467?
7. I have 3 pounds of fudge. If I eat 1/10 of a pound of fudge a day, how long will it take me to eat 3 pounds of fudge?
8. 7 2/3 + 9 5/8 = 9 2/3 + n
Fourth Grade Assessment — Student Copy
Fifth Grade
1. I have 498 books. How many more books would I need to get to have 505 books all together?
More challenging numbers, if needed: 2,995 3,015
2. I have 32 buckets with 10 rocks in each bucket. How many rocks do I have?
Numbers for later in the year, if needed: 78, 10 427, 10
3. 4 people want to share 7 cookies so that each person gets the same amount and there are no left overs. How much cookie should each person get?
Pay attention to how the student shows you their answer: with a picture; with words; with fraction symbols?
4. I have 6 large brownies. If I eat ¾ of a brownie each day, how many days will it take me to eat all 6 brownies?
5. Sasha had 5½ pounds of candy. She gave ¾ of a pound of candy to her sister. How many pounds of candy does Sasha have left?
6. 3001
- 2998
Give the problem above in this form at the beginning, middle and end of the year.
7. How many groups of ten are there in 467?
8. I have 12 pounds of fudge. If I eat 1/10 of a pound of fudge a day, how long will it take me to eat 12 pounds of fudge?
9. 100,000
- 2
Give the problem above in this form at the beginning, middle and end of the year.
10. 87 2/3 + 49 5/8 = 87 5/8 + n
Fifth Grade Assessment — Student Copy
Sixth Grade
1. I have 2,995 books. How many more books would I need to get to have 3,015 books all together?
More accessible numbers, if needed: 498, 502 998, 1,005
2. I have 78 buckets with 10 rocks in each bucket. How many rocks do I have?
More challenging numbers, if needed: 335, 10
3. 8 people want to share 5 cookies so that each person gets the same amount and there are no left overs. How much cookie should each person get?
4. I have 6 large brownies. If I eat ¾ of a brownie each day, how many days will it take me to eat all 6 brownies?
5. Sasha had 5 ½ pounds of candy. She gave ¾ of a pound of candy to her sister. How much candy does Sasha have left?
6. 3001
- 2998
Give the problem above in this form at the beginning, middle and end of the year.
7. It takes 0.1 of container of paint to paint 10 miles of highway. How much paint would we need to paint 10,000 miles of highway?
More challenging numbers for later in the year 0.1 1,000,000
8. How many groups of ten are there in 467?
9. 1,000,000
- 2
Give the problem above in this form at the beginning, middle and end of the year.
10. The high school principal has 123 pounds of fudge. He wants to gives 0.1 of a pound of fudge to each student at the high school. How many students could he give fudge to before his fudge runs out?
11. 87 2/3 + 49 5/8 = 87 5/8 + n
Sixth Grade Assessment — Student Copy
Assessing Mathematical Disposition — All grade levels
In addition to problems that assess math concepts, we also provide questions to assess students’ mathematical dispositions. Here are some questions about students’ mathematical dispositions that you could choose to ask at any grade level. Tell children to circle one answer for each question. These questions have not been tested with kindergarteners or early first graders. An alternative assessment that also has not been field tested is provided If you try these questions with young children, let us know how it goes!
1. I am good at math.
YES KINDA NOT REALLY NO
2. I can figure out how to solve math problems by myself.
USUALLY SOMETIMES SELDOM NEVER
3. When I grow up, I want to have a job where I use math.
YES MAYBE PROBABLY NOT NO