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California High School Proficiency Examination (CHSPE) Mathematics: Number Sense and Operations Syllabus
The Mathematics: Number Sense and Operations syllabus for California High School Proficiency Examination (CHSPE) in full: 4 chapters, 16 topics and 32 sub-topics, every one listed below, plus 50 Mathematics: Number Sense and Operations flashcards with answers.
Mathematics: Number Sense and Operations syllabus: all 4 chapters
Expand any chapter to see its topics and sub-topics.
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Whole Numbers and Integers
4 topics- Place Value and Number Representation
- Reading and writing large numbers
- Expanded and standard form
- Four Operations with Whole Numbers
- Multi-digit multiplication and division
- Order of operations
- Integer Operations
- Adding and subtracting signed numbers
- Multiplying and dividing negatives
- Factors, Multiples, and Primes
- GCF and LCM
- Prime factorization
- Place Value and Number Representation
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Fractions, Decimals, and Percents
4 topics- Operations with Fractions
- Adding and subtracting unlike fractions
- Multiplying and dividing fractions and mixed numbers
- Operations with Decimals
- Aligning and computing decimal sums
- Rounding and estimating decimals
- Percent Concepts
- Finding the percent of a number
- Percent increase and decrease
- Converting Among Forms
- Fraction to decimal to percent
- Comparing and ordering rational numbers
- Operations with Fractions
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Ratios, Proportions, and Rates
4 topics- Writing and Simplifying Ratios
- Part-to-part and part-to-whole ratios
- Equivalent ratios
- Solving Proportions
- Cross-multiplication
- Scale and similar-figure problems
- Unit Rates and Pricing
- Best-buy comparisons
- Speed, distance, and time rates
- Applications of Proportional Reasoning
- Recipes and mixtures
- Maps and models
- Writing and Simplifying Ratios
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Powers, Roots, and Estimation
4 topics- Exponents
- Evaluating powers
- Rules for multiplying and dividing powers
- Square Roots
- Perfect squares and their roots
- Estimating non-perfect roots
- Scientific Notation
- Writing very large and small numbers
- Computing in scientific notation
- Estimation and Reasonableness
- Rounding to estimate answers
- Checking results for reasonableness
- Exponents
California High School Proficiency Examination (CHSPE) Mathematics: Number Sense and Operations flashcards — 50 questions with answers
What is the place value of the digit 7 in the number 4,720?
Hundreds (7 represents 700).
Write the number 'three hundred five thousand, sixty' in standard form.
305,060
In a multi-digit number, how does the value of a digit change as it moves one place to the left?
It becomes 10 times greater than it would be one place to the right.
Write 2,408 in expanded form.
2,000 + 400 + 0 + 8 (i.e., 2,000 + 400 + 8).
What are the four basic operations on whole numbers and their result names?
Addition (sum), subtraction (difference), multiplication (product), and division (quotient).
In long division, what is the relationship among dividend, divisor, quotient, and remainder?
Dividend = (divisor x quotient) + remainder.
State the order of operations (PEMDAS).
Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right).
What is the result of adding two negative integers, such as (-6) + (-4)?
A negative number: -10. Add the absolute values and keep the negative sign.
What is the sign rule for multiplying or dividing two integers with different signs?
The result is negative (e.g., (-3) x 4 = -12).
What is the sign rule for multiplying or dividing two integers with the same sign?
The result is positive (e.g., (-3) x (-4) = 12).
How do you subtract a negative integer, as in 5 - (-3)?
Adding the opposite: 5 - (-3) = 5 + 3 = 8.
What is the absolute value of a number, and what is |-9|?
The distance of a number from zero on the number line; |-9| = 9.
What is a factor of a number?
A whole number that divides the number evenly with no remainder.
What is a multiple of a number?
The product of that number and any whole number (e.g., multiples of 4: 4, 8, 12, 16, ...).
Define a prime number and give the smallest one.
A whole number greater than 1 with exactly two factors, 1 and itself; the smallest prime is 2.
Define a composite number.
A whole number greater than 1 that has more than two factors (i.e., it is not prime).
What is the prime factorization of 36?
2 x 2 x 3 x 3, or 2^2 x 3^2.
What is the greatest common factor (GCF) of 12 and 18?
6.
What is the least common multiple (LCM) of 4 and 6?
12.
How do you add or subtract fractions with unlike denominators?
Find a common denominator, rewrite each fraction with it, then add or subtract the numerators and keep the denominator.
Show the other 30 Mathematics: Number Sense and Operations flashcards
How do you multiply two fractions?
Multiply the numerators together and the denominators together, then simplify (e.g., 2/3 x 4/5 = 8/15).
How do you divide by a fraction, as in (3/4) ÷ (2/5)?
Multiply by the reciprocal of the divisor: 3/4 x 5/2 = 15/8.
How do you convert the mixed number 3 1/4 to an improper fraction?
Multiply whole number by denominator and add numerator: (3x4+1)/4 = 13/4.
How do you simplify a fraction to lowest terms?
Divide both numerator and denominator by their greatest common factor.
How do you add or subtract decimals?
Line up the decimal points, then add or subtract as with whole numbers, keeping the decimal point in the same column.
How do you place the decimal point when multiplying 2.5 x 0.3?
Multiply as whole numbers (25 x 3 = 75), then place the decimal so the product has as many decimal places as the factors combined (2 places): 0.75.
When dividing by a decimal, what should you do first?
Move the divisor's decimal point to make it a whole number, and move the dividend's decimal point the same number of places.
What does 'percent' mean?
Per hundred; a percent is a ratio comparing a number to 100 (e.g., 25% = 25/100).
What is the formula for finding a percent of a number?
Part = percent (as a decimal) x whole. For example, 20% of 50 = 0.20 x 50 = 10.
How do you find what percent one number is of another, e.g., 15 out of 60?
Divide the part by the whole and multiply by 100: 15/60 = 0.25 = 25%.
How do you calculate a percent increase or decrease?
Divide the amount of change by the original amount, then multiply by 100.
How do you convert a decimal to a percent?
Multiply by 100 and add the percent sign (e.g., 0.45 = 45%).
How do you convert a percent to a fraction in lowest terms, e.g., 40%?
Write it over 100 and simplify: 40/100 = 2/5.
How do you convert a fraction to a decimal?
Divide the numerator by the denominator (e.g., 3/8 = 0.375).
What is a ratio, and how can the ratio 'of 8 to 12' be written?
A comparison of two quantities; it can be written as 8 to 12, 8:12, or 8/12, and simplified to 2:3.
How do you simplify the ratio 15:25?
Divide both terms by their GCF (5): 3:5.
What is a proportion?
An equation stating that two ratios are equal, such as a/b = c/d.
How do you solve a proportion using cross multiplication, e.g., x/4 = 6/8?
Cross multiply: 8x = 24, so x = 3.
What is a unit rate?
A rate with a denominator of 1, such as miles per 1 hour or price per 1 item.
How do you find the better buy between $4.50 for 3 lbs and $7.00 for 5 lbs?
Find unit prices: $4.50/3 = $1.50/lb and $7.00/5 = $1.40/lb; the 5-lb option is the better buy.
If 3 pens cost $1.80, what proportional reasoning gives the cost of 7 pens?
Unit price is $1.80/3 = $0.60 per pen; 7 x $0.60 = $4.20.
On a map, 1 inch = 50 miles. How many miles do 3.5 inches represent?
3.5 x 50 = 175 miles.
What does an exponent tell you, as in 5^3?
It tells how many times the base is used as a factor: 5^3 = 5 x 5 x 5 = 125.
What is the value of any nonzero number raised to the power of 0?
1 (e.g., 7^0 = 1).
What are the product and quotient rules for exponents with the same base?
Add exponents when multiplying (a^m x a^n = a^(m+n)); subtract when dividing (a^m / a^n = a^(m-n)).
What is a square root, and what is the square root of 49?
A number that, when multiplied by itself, gives the original number; √49 = 7.
List the first five perfect squares (of 1 through 5).
1, 4, 9, 16, and 25.
What is scientific notation?
A way to write numbers as a x 10^n, where 1 ≤ a < 10 and n is an integer.
Write 56,000 in scientific notation.
5.6 x 10^4.
Estimate 312 x 49 using rounding, and judge reasonableness.
Round to 300 x 50 = 15,000; an exact answer near 15,000 (15,288) is reasonable.
California High School Proficiency Examination (CHSPE) Mathematics: Number Sense and Operations FAQ
What is in the California High School Proficiency Examination (CHSPE) Mathematics: Number Sense and Operations syllabus?
California High School Proficiency Examination (CHSPE) Mathematics: Number Sense and Operations is split into 4 chapters: Whole Numbers and Integers, Fractions, Decimals, and Percents, Ratios, Proportions, and Rates and Powers, Roots, and Estimation. Together they contain 16 topics and 32 sub-topics.
How many chapters are in California High School Proficiency Examination (CHSPE) Mathematics: Number Sense and Operations?
4 chapters, containing 16 topics and 32 sub-topics. The largest chapter is Whole Numbers and Integers, with 4 topics.
Are there flashcards for California High School Proficiency Examination (CHSPE) Mathematics: Number Sense and Operations?
Yes — a 50-card Mathematics: Number Sense and Operations deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.