ABCTE Multiple Subject –
Mathematics 2026 Expert
Verifed Ace the Test
Understand the structure of the real number system - ANSWER
✔✔(including whole numbers, integers, rational and irrationals) and be
able to perform operations within the Real Number system.
Examples:
Natural Numbers1, 2, 3, 4, ...,
Whole Numbers 0,1,2,3,4...
Integers...-3,-2,-1,0,1,2,3,...
,Rational NumbersNumbers that can be expressed as fractions. 2/3 is
rational.
Irrational NumbersNumbers that can not be written as fractions.
3.14159... is irrational.
Composite numbers have more than two factors but not an infinite
number of factors.
All even numbers (except the number two) are composite, since they
can all be divided by two.
Understand base ten place value - ANSWER ✔✔and identify the
place value for each digit in whole numbers and decimals
Example:
1, 10, 100, 1000....
Compare and order real numbers - ANSWER ✔✔(including irrationals
and rationals, in fraction and decimal form) using the appropriate
symbols, =, <, >.
Example:
2=2, 1< 2, 2>1
,Identify and represent on a number line - ANSWER ✔✔whole
numbers, fractions, decimals, mixed numbers, and positive and negative
integers.
Understand the difference between - ANSWER ✔✔rote and rational
counting (one-to-one correspondence).
Example:
Rational counting "1penny, 2 pennies"
Rote counting "1,2,3,4,5 6,7,8,9,10".
Understand the relationship between - ANSWER ✔✔number lines,
counting and measurement.
Round off whole numbers - ANSWER ✔✔to the nearest ten, hundred,
or thousand, ten thousand, or hundred thousand and round off decimals
to the nearest tenth, hundredth, or thousandth.
Example:
Round 23, 36, 55, and 99
Answer 20, 40, 60, 100
Make reasonable estimates - ANSWER ✔✔when comparing larger or
smaller numbers e.g., by working with orders of magnitude.
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STATEMENT. ALL RIGHTS RESERVED
3
, Estimate and round - ANSWER ✔✔very large (e.g., millions) and very
small (e.g., thousandths) numbers.
Example:
6,852,783 rounded to the nearest million is 7,000,000
If less than 5, round down, but it more than 5, round up
232.423 = 232.4
Understand number theory concepts - ANSWER ✔✔of primes,
factors, multiples, and divisibility rules and understand relationships
among the concepts (e.g., perform a prime factorization on a number
less than 100.)
Examples:
Prime numbers 2, 3, 5 are ______ because they have two different
factors (2 = 1 x 2), (3 = 1 x 3), (5 = 1 x 5)
Find factors for 6, the factors of 6 are 1, 2, 3 and 6.
The number 6 can be multipied by 1, 2, 3 and 6 and divided as well by
those numbers.
Recognize name and compare - ANSWER ✔✔unit fractions.
Examples:
Mathematics 2026 Expert
Verifed Ace the Test
Understand the structure of the real number system - ANSWER
✔✔(including whole numbers, integers, rational and irrationals) and be
able to perform operations within the Real Number system.
Examples:
Natural Numbers1, 2, 3, 4, ...,
Whole Numbers 0,1,2,3,4...
Integers...-3,-2,-1,0,1,2,3,...
,Rational NumbersNumbers that can be expressed as fractions. 2/3 is
rational.
Irrational NumbersNumbers that can not be written as fractions.
3.14159... is irrational.
Composite numbers have more than two factors but not an infinite
number of factors.
All even numbers (except the number two) are composite, since they
can all be divided by two.
Understand base ten place value - ANSWER ✔✔and identify the
place value for each digit in whole numbers and decimals
Example:
1, 10, 100, 1000....
Compare and order real numbers - ANSWER ✔✔(including irrationals
and rationals, in fraction and decimal form) using the appropriate
symbols, =, <, >.
Example:
2=2, 1< 2, 2>1
,Identify and represent on a number line - ANSWER ✔✔whole
numbers, fractions, decimals, mixed numbers, and positive and negative
integers.
Understand the difference between - ANSWER ✔✔rote and rational
counting (one-to-one correspondence).
Example:
Rational counting "1penny, 2 pennies"
Rote counting "1,2,3,4,5 6,7,8,9,10".
Understand the relationship between - ANSWER ✔✔number lines,
counting and measurement.
Round off whole numbers - ANSWER ✔✔to the nearest ten, hundred,
or thousand, ten thousand, or hundred thousand and round off decimals
to the nearest tenth, hundredth, or thousandth.
Example:
Round 23, 36, 55, and 99
Answer 20, 40, 60, 100
Make reasonable estimates - ANSWER ✔✔when comparing larger or
smaller numbers e.g., by working with orders of magnitude.
COPYRIGHT©NINJANERD 2025/2026. YEAR PUBLISHED 2026. COMPANY REGISTRATION NUMBER: 619652435. TERMS OF USE. PRIVACY
STATEMENT. ALL RIGHTS RESERVED
3
, Estimate and round - ANSWER ✔✔very large (e.g., millions) and very
small (e.g., thousandths) numbers.
Example:
6,852,783 rounded to the nearest million is 7,000,000
If less than 5, round down, but it more than 5, round up
232.423 = 232.4
Understand number theory concepts - ANSWER ✔✔of primes,
factors, multiples, and divisibility rules and understand relationships
among the concepts (e.g., perform a prime factorization on a number
less than 100.)
Examples:
Prime numbers 2, 3, 5 are ______ because they have two different
factors (2 = 1 x 2), (3 = 1 x 3), (5 = 1 x 5)
Find factors for 6, the factors of 6 are 1, 2, 3 and 6.
The number 6 can be multipied by 1, 2, 3 and 6 and divided as well by
those numbers.
Recognize name and compare - ANSWER ✔✔unit fractions.
Examples:
