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Math Problems for Elementary Education Students: Final Exam, Exams of Elementary Mathematics

A collection of math problems for elementary education students in their final exam. The problems cover various topics such as weighing objects, venn diagrams, work rate, charged particle model, multiplication table, area measurement, prime factorization, place value system, mental math, car number-line model, and percentages.

Typology: Exams

2012/2013

Uploaded on 03/31/2013

parthavi
parthavi 🇮🇳

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Prof. S. Brick Math for Elem Ed I; Final Math 201
Summer ’04 section 101
Print your name:
Show all of your work. Explain your reasoning. NO CALCULATORS.
1. Your class has a balance scale to weigh objects. The scale has two pans, one for the
objects to be weighed, the other to place pre-measured weights on. The pre-measured
weights consist of three 1-gram weights, three 4-gram weights, and three 16-gram weights.
What is the range of all the possible weights of possible objects that the scale can accurately
measure using this collection of weights ? Why ? What numeration system does this
activity explore ? Explain all of your reasoning.
2. A survey of 109 students shows that 72 love math, 56 love history, yet 5 do not love
either of the two subjects. Draw and use a Venn diagram to describe this situation. Make
sure you label all the sub-regions correctly, both in words and numbers. Show and explain
all of your steps.
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Prof. S. Brick Math for Elem Ed I; Final Math 201

Summer ’04 section 101

Print your name:

Show all of your work. Explain your reasoning. NO CALCULATORS.

  1. Your class has a balance scale to weigh objects. The scale has two pans, one for the objects to be weighed, the other to place pre-measured weights on. The pre-measured weights consist of three 1-gram weights, three 4-gram weights, and three 16-gram weights. What is the range of all the possible weights of possible objects that the scale can accurately measure using this collection of weights? Why? What numeration system does this activity explore? Explain all of your reasoning.
  2. A survey of 109 students shows that 72 love math, 56 love history, yet 5 do not love either of the two subjects. Draw and use a Venn diagram to describe this situation. Make sure you label all the sub-regions correctly, both in words and numbers. Show and explain all of your steps.
  1. If four men working six hours can dig five holes, how long does it take one man to dig one hole? Explain all of your steps. (Give your answer in hours and minutes.)
  2. Use the charged particle model to explain the computations 4 − (−5). Show and explain all the steps, using several different pictures and words for each step.
  1. Find the prime factorizations for 132 and 495 and use them to find their GCD. Do not use the Euclidean algorithm. Show and explain all of your steps.
  2. Working in base seven, compute the sum of 655 and 1534 using place value cards. Use several figures to show how your calculation progresses. Show and explain all of your steps.
  1. You make a purchase totaling $18.20. The sales tax is 9%. Explain how to use mental math to find the sales tax. Give a two step method that involves no explicit multiplication, but only moving the decimal place and subtraction, yet finds the tax exactly. (Use the “ Up” rule in your calculation for any tenths of cents.) Show and explain all of your steps.
  2. Explain how the car number-line model works for the problems 50 + (−30) and 50 − 30. Draw number-lines and be explicit about the difference between the problems. Explain.
  1. Use an area model to compute 23 − 12. Do not work the problem algebraically. Instead, let your model do all of the work. Show and explain all of your steps.
  2. Suppose A and B are positive. If 56% of A equals 28% of B, find the ratio of A to A + B. Do not assign any numerical values to either A or B. Show and explain all of your steps.

SCRATCH PAPER below– will not be graded