MATE 3050 Midterm Exam Study Guide
Standards for Mathematical Content - ANSWER •K-8 standards different from grade
level to grade level
•High school standards presented by conceptual theme
•WHAT we do in math
Standards for Mathematical Practice - ANSWER •Carry across all grade levels
•Describe habits of mind of "great mathematicians"
•HOW we do math
Eight Math Practice Standards - ANSWER 1.Make sense of problems and persevere in
solving them
-Students demonstrate this standard by working on a difficult problem, finding a way to
solve the problem, and working on the problem until it is solved.
2. Reason abstractly and quantitatively
-Students demonstrate this standard by drawing a representation of a problem, and
using manipulatives to figure out what to do with data on their own, instead of boxing the
data into one type of organization. Then, the students draw their thinking, with and
without traditional number sentences.
3. Construct viable arguments and critique the reasoning of others
-Students demonstrate this standard by talking about math and using mathematical
vocabulary inside and outside of the classroom
4. Model with mathematics
-Students demonstrate this standard by using math to solve real-world problems. For
an example, a student can use math while in science class when they are asked to
create a graph.
5. Use appropriate tools strategically
-Students demonstrate this standard by exploring different tools and choosing which
one to use to solve a problem. If a student has to solve a problem regarding height, they
can choose from a variety of tools to use such as a yard stick, a ruler and a tape
measurer.
6. Attend to precision
, -Students demonstrate this standard by using correct and precise language in math.
Students also demonstrate this by showing all of their work after completing a problem.
7. Look for and make use of structure
-Students demonstrate this standard by being familiar with breaking apart problems
and numbers into familiar relationships.
8. Look for and express regularity in repeated reasoning
-Students demonstrate this standard by contouring to the next concept after mastering
the one they have been working on.
Early counting skills: Count and Land - ANSWER when children first learn to count, they
think of quantities as a series of one, and another one, and another one, and so on. In a
sense, they are labeling each counter rather than determining how many there are
altogether. Their focus is on touching each object and saying the right numbers. Their
answer is whatever number they happen to land on when they have finished pointing at
each object.
Early counting skills: Rote Counting - ANSWER When you count on correctly. Example:
"1, 2, 3, 4, 5"
Early counting skills: One-to-one correspondence - ANSWER Counting objects by saying
number words in a one-to-one correspondence with the objects
What students can do: counting up and back (line 5 chairs up and count 5 students as
they sit in the chairs)
Early counting skills: Conservation of Number - ANSWER Knowing that a number means
an amount, and that amount doesn't change no matter how you move the objects
What students can do: Matching games (use cards with dots, have the student recreate
the pattern with tokens. The pattern looks different but it's the same amount)
Early counting skills: Cardinality (inclusion) - ANSWER Understanding that the last
number word said when counting tells how many objects have been counted
What students can do: Play a counting game. They collect items around the room bases
on a certain number chosen
Early counting skills: Keeping track - ANSWER Being able to keep track of items that
have already been counted
What students can do: have the students count different collections of objects
Early counting skills: One more/one less - ANSWER -Knows one more in sequence
without counting
-Knows one less in sequence without counting
Standards for Mathematical Content - ANSWER •K-8 standards different from grade
level to grade level
•High school standards presented by conceptual theme
•WHAT we do in math
Standards for Mathematical Practice - ANSWER •Carry across all grade levels
•Describe habits of mind of "great mathematicians"
•HOW we do math
Eight Math Practice Standards - ANSWER 1.Make sense of problems and persevere in
solving them
-Students demonstrate this standard by working on a difficult problem, finding a way to
solve the problem, and working on the problem until it is solved.
2. Reason abstractly and quantitatively
-Students demonstrate this standard by drawing a representation of a problem, and
using manipulatives to figure out what to do with data on their own, instead of boxing the
data into one type of organization. Then, the students draw their thinking, with and
without traditional number sentences.
3. Construct viable arguments and critique the reasoning of others
-Students demonstrate this standard by talking about math and using mathematical
vocabulary inside and outside of the classroom
4. Model with mathematics
-Students demonstrate this standard by using math to solve real-world problems. For
an example, a student can use math while in science class when they are asked to
create a graph.
5. Use appropriate tools strategically
-Students demonstrate this standard by exploring different tools and choosing which
one to use to solve a problem. If a student has to solve a problem regarding height, they
can choose from a variety of tools to use such as a yard stick, a ruler and a tape
measurer.
6. Attend to precision
, -Students demonstrate this standard by using correct and precise language in math.
Students also demonstrate this by showing all of their work after completing a problem.
7. Look for and make use of structure
-Students demonstrate this standard by being familiar with breaking apart problems
and numbers into familiar relationships.
8. Look for and express regularity in repeated reasoning
-Students demonstrate this standard by contouring to the next concept after mastering
the one they have been working on.
Early counting skills: Count and Land - ANSWER when children first learn to count, they
think of quantities as a series of one, and another one, and another one, and so on. In a
sense, they are labeling each counter rather than determining how many there are
altogether. Their focus is on touching each object and saying the right numbers. Their
answer is whatever number they happen to land on when they have finished pointing at
each object.
Early counting skills: Rote Counting - ANSWER When you count on correctly. Example:
"1, 2, 3, 4, 5"
Early counting skills: One-to-one correspondence - ANSWER Counting objects by saying
number words in a one-to-one correspondence with the objects
What students can do: counting up and back (line 5 chairs up and count 5 students as
they sit in the chairs)
Early counting skills: Conservation of Number - ANSWER Knowing that a number means
an amount, and that amount doesn't change no matter how you move the objects
What students can do: Matching games (use cards with dots, have the student recreate
the pattern with tokens. The pattern looks different but it's the same amount)
Early counting skills: Cardinality (inclusion) - ANSWER Understanding that the last
number word said when counting tells how many objects have been counted
What students can do: Play a counting game. They collect items around the room bases
on a certain number chosen
Early counting skills: Keeping track - ANSWER Being able to keep track of items that
have already been counted
What students can do: have the students count different collections of objects
Early counting skills: One more/one less - ANSWER -Knows one more in sequence
without counting
-Knows one less in sequence without counting
