You will find an excellent and extensive listing of sample test questions on the New York State Education Department website. These sample questions are categorized from 3rd through to8th grade and they are aligned to the Common Core For Mathematics Standards.
The practice quizzes below include around 10 questions. They might last a little longer as the questions sometimes change based on the answers given to previous questions.
Some of the practice questions include hints and explanations. These are only shown when previous answers in the quiz suggest they might be required. The first set of quizzes are on addition and cover the often tricky "bridging over" 10 and multiples of 10. The hints show how 10 and multiples of 10 can be used as a "stepping stone" to get to the answer.
Bridging over 10 e.g. 8 + 5
Bridging over 20 e.g. 17 + 6
Bridging over Multiples of 10 e.g. 58 + 4
Rounding Decimals e.g. 3.234 to nearest hundredth
Fractions on a Number Line e.g. halves, thirds, fourths, sixths, eighths
Integer Rules e.g. 3 - (-2) = 5
You will find a short 4th Grade Test here. (Note - This test is not aligned to the Common Core For Mathematics)