Core Knowledge
A coefficient is a specified factor of a specified part of a term.
For example, in 4a, the coefficient of a is 4.
While we generally use "coefficient" to refer to the numeric part, it can technically refer to any factor of the specified part.
Example
Answer the following:
a)
$$\text{What is the coefficient of } a \text{ in the term } 4a?$$
$$4$$
b)
$$\text{What is the coefficient of } b \text{ in the term } 5b?$$
$$5$$
Question 1
On your whiteboards, answer the following:
a)
$$\text{What is the coefficient of } a \text{ in the term } 6a?$$
b)
$$\text{What is the coefficient of } y \text{ in the term } 9y?$$
c)
$$\text{What is the coefficient of } m \text{ in the term } 3m?$$
d)
$$\text{What is the coefficient of } n \text{ in the term } 11n?$$
Answers
Show me your whiteboards.
a)
$$\text{What is the coefficient of } a \text{ in the term } 6a?$$
$$6$$
b)
$$\text{What is the coefficient of } y \text{ in the term } 9y?$$
$$9$$
c)
$$\text{What is the coefficient of } m \text{ in the term } 3m?$$
$$3$$
d)
$$\text{What is the coefficient of } n \text{ in the term } 11n?$$
$$11$$
Question 2
You haven't seen questions exactly like this before, but using what you know, on your whiteboards, answer the following:
a)
$$\text{What is the coefficient of } x \text{ in the term } -3x?$$
b)
$$\text{What is the coefficient of } x \text{ in the term } 3x^2?$$
c)
$$\text{What is the coefficient of } x \text{ in the term } 0.5x?$$
d)
$$\text{What is the coefficient of } x^2 \text{ in the term } 0.5x^2?$$
Answers
Show me your whiteboards.
a)
$$\text{What is the coefficient of } x \text{ in the term } -3x?$$
$$-3$$
b)
$$\text{What is the coefficient of } x \text{ in the term } 3x^2?$$
$$3$$
c)
$$\text{What is the coefficient of } x \text{ in the term } 0.5x?$$
$$0.5$$
d)
$$\text{What is the coefficient of } x^2 \text{ in the term } 0.5x^2?$$
$$0.5$$
Core Knowledge
We can identify numeric coefficients in composite terms containing multiple variables.
For example, in 5ab, the coefficient of ab is 5.
Example
Answer the following:
a)
$$\text{What is the coefficient of } ab \text{ in the term } 5ab?$$
$$5$$
b)
$$\text{What is the coefficient of } xy \text{ in the term } 8xy?$$
$$8$$
Question 3
On your whiteboards, answer the following:
a)
$$\text{What is the coefficient of } ab \text{ in the term } 3ab?$$
b)
$$\text{What is the coefficient of } xy \text{ in the term } 9xy?$$
c)
$$\text{What is the coefficient of } cd \text{ in the term } 4cd?$$
d)
$$\text{What is the coefficient of } ab^2 \text{ in the term } 7ab^2?$$
Answers
Show me your whiteboards.
a)
$$\text{What is the coefficient of } ab \text{ in the term } 3ab?$$
$$3$$
b)
$$\text{What is the coefficient of } xy \text{ in the term } 9xy?$$
$$9$$
c)
$$\text{What is the coefficient of } cd \text{ in the term } 4cd?$$
$$4$$
d)
$$\text{What is the coefficient of } ab^2 \text{ in the term } 7ab^2?$$
$$7$$
Question 4
You haven't seen questions exactly like this before, but using what you know, on your whiteboards, answer the following:
a)
$$\text{What is the coefficient of } xy \text{ in the term } -2xy?$$
b)
$$\text{What is the coefficient of } ab^2 \text{ in the term } 5ab^2?$$
c)
$$\text{What is the coefficient of } pq \text{ in the term } 0.5pq?$$
d)
$$\text{What is the coefficient of } xy^2 \text{ in the term } 0.5xy^2?$$
Answers
Show me your whiteboards.
a)
$$\text{What is the coefficient of } xy \text{ in the term } -2xy?$$
$$-2$$
b)
$$\text{What is the coefficient of } ab^2 \text{ in the term } 5ab^2?$$
$$5$$
c)
$$\text{What is the coefficient of } pq \text{ in the term } 0.5pq?$$
$$0.5$$
d)
$$\text{What is the coefficient of } xy^2 \text{ in the term } 0.5xy^2?$$
$$0.5$$
Core Knowledge
When no numeric coefficient is written in front of a term, the coefficient is 1.
For example, in the term a, the coefficient of a is 1.
In the term xy, the coefficient of xy is 1.
Example
Answer the following:
a)
$$\text{What is the coefficient of } a \text{ in the term } a?$$
$$1$$
b)
$$\text{What is the coefficient of } xy \text{ in the term } xy?$$
$$1$$
Question 5
On your whiteboards, answer the following:
a)
$$\text{What is the coefficient of } b \text{ in the term } b?$$
b)
$$\text{What is the coefficient of } x \text{ in the term } x?$$
c)
$$\text{What is the coefficient of } ab \text{ in the term } ab?$$
d)
$$\text{What is the coefficient of } pq \text{ in the term } pq?$$
Answers
Show me your whiteboards.
a)
$$\text{What is the coefficient of } b \text{ in the term } b?$$
$$1$$
b)
$$\text{What is the coefficient of } x \text{ in the term } x?$$
$$1$$
c)
$$\text{What is the coefficient of } ab \text{ in the term } ab?$$
$$1$$
d)
$$\text{What is the coefficient of } pq \text{ in the term } pq?$$
$$1$$
Core Knowledge
When finding coefficients in composite terms, we must be precise about which part we're finding the coefficient of.
In 4ab, the coefficient of b is 4a, while the coefficient of a is 4b.
Example
Answer the following:
a)
$$\text{What is the coefficient of } b \text{ in the term } 4ab?$$
$$4a$$
b)
$$\text{What is the coefficient of } a \text{ in the term } 4ab?$$
$$4b$$
Question 6
On your whiteboards, answer the following:
a)
$$\text{What is the coefficient of } b \text{ in the term } 6ab?$$
b)
$$\text{What is the coefficient of } a \text{ in the term } 6ab?$$
c)
$$\text{What is the coefficient of } q \text{ in the term } 3pq^2?$$
d)
$$\text{What is the coefficient of } p \text{ in the term } 3pq^2?$$
Answers
Show me your whiteboards.
a)
$$\text{What is the coefficient of } b \text{ in the term } 6ab?$$
$$6a$$
b)
$$\text{What is the coefficient of } a \text{ in the term } 6ab?$$
$$6b$$
c)
$$\text{What is the coefficient of } q \text{ in the term } 3pq^2?$$
$$3p$$
d)
$$\text{What is the coefficient of } p \text{ in the term } 3pq^2?$$
$$3q^2$$
Question 7
You haven't seen questions exactly like this before, but using what you know, on your whiteboards, answer the following:
a)
$$\text{What is the coefficient of } y \text{ in the term } -5xy?$$
b)
$$\text{What is the coefficient of } x \text{ in the term } -5xy?$$
c)
$$\text{What is the coefficient of } b \text{ in the term } 0.5ab^2?$$
d)
$$\text{What is the coefficient of } a \text{ in the term } 0.5ab^2?$$
Answers
Show me your whiteboards.
a)
$$\text{What is the coefficient of } y \text{ in the term } -5xy?$$
$$-5x$$
b)
$$\text{What is the coefficient of } x \text{ in the term } -5xy?$$
$$-5y$$
c)
$$\text{What is the coefficient of } b \text{ in the term } 0.5ab^2?$$
$$0.5a$$
d)
$$\text{What is the coefficient of } a \text{ in the term } 0.5ab^2?$$
$$0.5b^2$$
Core Knowledge
Coefficients can be fractions.
When a fraction is written explicitly before an algebraic term, such as (2/3)a, the coefficient is the fraction itself, in this case 2/3.
Example
Answer the following:
a)
$$\text{What is the coefficient of } a \text{ in the term } \dfrac{2}{3}a?$$
$$\dfrac{2}{3}$$
b)
$$\text{What is the coefficient of } b \text{ in the term } \dfrac{3}{4}b?$$
$$\dfrac{3}{4}$$
Question 8
On your whiteboards, answer the following:
a)
$$\text{What is the coefficient of } a \text{ in the term } \dfrac{2}{5}a?$$
b)
$$\text{What is the coefficient of } b \text{ in the term } \dfrac{3}{7}b?$$
c)
$$\text{What is the coefficient of } x \text{ in the term } \dfrac{5}{8}x?$$
d)
$$\text{What is the coefficient of } z \text{ in the term } \dfrac{2}{9}z?$$
Answers
Show me your whiteboards.
a)
$$\text{What is the coefficient of } a \text{ in the term } \dfrac{2}{5}a?$$
$$\dfrac{2}{5}$$
b)
$$\text{What is the coefficient of } b \text{ in the term } \dfrac{3}{7}b?$$
$$\dfrac{3}{7}$$
c)
$$\text{What is the coefficient of } x \text{ in the term } \dfrac{5}{8}x?$$
$$\dfrac{5}{8}$$
d)
$$\text{What is the coefficient of } z \text{ in the term } \dfrac{2}{9}z?$$
$$\dfrac{2}{9}$$
Question 9
You haven't seen questions exactly like this before, but using what you know, on your whiteboards, answer the following:
a)
$$\text{What is the coefficient of } x \text{ in the term } -\dfrac{2}{3}x?$$
b)
$$\text{What is the coefficient of } x^2 \text{ in the term } -\dfrac{2}{3}x^2?$$
c)
$$\text{What is the coefficient of } a \text{ in the term } \dfrac{5}{6}a?$$
d)
$$\text{What is the coefficient of } z \text{ in the term } -\dfrac{3}{4}z?$$
Answers
Show me your whiteboards.
a)
$$\text{What is the coefficient of } x \text{ in the term } -\dfrac{2}{3}x?$$
$$-\dfrac{2}{3}$$
b)
$$\text{What is the coefficient of } x^2 \text{ in the term } -\dfrac{2}{3}x^2?$$
$$-\dfrac{2}{3}$$
c)
$$\text{What is the coefficient of } a \text{ in the term } \dfrac{5}{6}a?$$
$$\dfrac{5}{6}$$
d)
$$\text{What is the coefficient of } z \text{ in the term } -\dfrac{3}{4}z?$$
$$-\dfrac{3}{4}$$
Core Knowledge
When an algebraic term is written with the variable in the numerator, such as 2a/3, the coefficient is still the numeric fraction.
In 2a/3, the coefficient of a is 2/3.
Example
Answer the following:
a)
$$\text{What is the coefficient of } a \text{ in the term } \dfrac{2a}{3}?$$
$$\dfrac{2}{3}$$
b)
$$\text{What is the coefficient of } b \text{ in the term } \dfrac{3b}{4}?$$
$$\dfrac{3}{4}$$
Question 10
On your whiteboards, answer the following:
a)
$$\text{What is the coefficient of } a \text{ in the term } \dfrac{2a}{5}?$$
b)
$$\text{What is the coefficient of } b \text{ in the term } \dfrac{3b}{7}?$$
c)
$$\text{What is the coefficient of } x \text{ in the term } \dfrac{5x}{8}?$$
d)
$$\text{What is the coefficient of } z \text{ in the term } \dfrac{2z}{9}?$$
Answers
Show me your whiteboards.
a)
$$\text{What is the coefficient of } a \text{ in the term } \dfrac{2a}{5}?$$
$$\dfrac{2}{5}$$
b)
$$\text{What is the coefficient of } b \text{ in the term } \dfrac{3b}{7}?$$
$$\dfrac{3}{7}$$
c)
$$\text{What is the coefficient of } x \text{ in the term } \dfrac{5x}{8}?$$
$$\dfrac{5}{8}$$
d)
$$\text{What is the coefficient of } z \text{ in the term } \dfrac{2z}{9}?$$
$$\dfrac{2}{9}$$
Question 11
You haven't seen questions exactly like this before, but using what you know, on your whiteboards, answer the following:
a)
$$\text{What is the coefficient of } x \text{ in the term } \dfrac{-2x}{3}?$$
b)
$$\text{What is the coefficient of } x^2 \text{ in the term } \dfrac{-2x^2}{3}?$$
c)
$$\text{What is the coefficient of } a \text{ in the term } \dfrac{5a}{6}?$$
d)
$$\text{What is the coefficient of } z \text{ in the term } \dfrac{-3z}{4}?$$
Answers
Show me your whiteboards.
a)
$$\text{What is the coefficient of } x \text{ in the term } \dfrac{-2x}{3}?$$
$$-\dfrac{2}{3}$$
b)
$$\text{What is the coefficient of } x^2 \text{ in the term } \dfrac{-2x^2}{3}?$$
$$-\dfrac{2}{3}$$
c)
$$\text{What is the coefficient of } a \text{ in the term } \dfrac{5a}{6}?$$
$$\dfrac{5}{6}$$
d)
$$\text{What is the coefficient of } z \text{ in the term } \dfrac{-3z}{4}?$$
$$-\dfrac{3}{4}$$
Core Knowledge
When a variable appears in the numerator without an explicit numeric coefficient, the coefficient is the implied 1 divided by the denominator.
In a/3, the coefficient of a is 1/3.
Example
Answer the following:
a)
$$\text{What is the coefficient of } a \text{ in the term } \dfrac{a}{3}?$$
$$\dfrac{1}{3}$$
b)
$$\text{What is the coefficient of } b \text{ in the term } \dfrac{b}{4}?$$
$$\dfrac{1}{4}$$
Question 12
On your whiteboards, answer the following:
a)
$$\text{What is the coefficient of } a \text{ in the term } \dfrac{a}{2}?$$
b)
$$\text{What is the coefficient of } b \text{ in the term } \dfrac{b}{6}?$$
c)
$$\text{What is the coefficient of } m \text{ in the term } \dfrac{m}{8}?$$
d)
$$\text{What is the coefficient of } n \text{ in the term } \dfrac{n}{9}?$$
Answers
Show me your whiteboards.
a)
$$\text{What is the coefficient of } a \text{ in the term } \dfrac{a}{2}?$$
$$\dfrac{1}{2}$$
b)
$$\text{What is the coefficient of } b \text{ in the term } \dfrac{b}{6}?$$
$$\dfrac{1}{6}$$
c)
$$\text{What is the coefficient of } m \text{ in the term } \dfrac{m}{8}?$$
$$\dfrac{1}{8}$$
d)
$$\text{What is the coefficient of } n \text{ in the term } \dfrac{n}{9}?$$
$$\dfrac{1}{9}$$
Question 13
You haven't seen questions exactly like this before, but using what you know, on your whiteboards, answer the following:
a)
$$\text{What is the coefficient of } x \text{ in the term } \dfrac{-x}{3}?$$
b)
$$\text{What is the coefficient of } x^2 \text{ in the term } \dfrac{x^2}{5}?$$
c)
$$\text{What is the coefficient of } p \text{ in the term } \dfrac{-p}{4}?$$
d)
$$\text{What is the coefficient of } q^2 \text{ in the term } \dfrac{-q^2}{6}?$$
Answers
Show me your whiteboards.
a)
$$\text{What is the coefficient of } x \text{ in the term } \dfrac{-x}{3}?$$
$$-\dfrac{1}{3}$$
b)
$$\text{What is the coefficient of } x^2 \text{ in the term } \dfrac{x^2}{5}?$$
$$\dfrac{1}{5}$$
c)
$$\text{What is the coefficient of } p \text{ in the term } \dfrac{-p}{4}?$$
$$-\dfrac{1}{4}$$
d)
$$\text{What is the coefficient of } q^2 \text{ in the term } \dfrac{-q^2}{6}?$$
$$-\dfrac{1}{6}$$
📝 Core Knowledge Review - Write in your books:
What is a coefficient: A coefficient is the number part of a term. In $4a$, the coefficient of $a$ is $4$.
Coefficient of 1: When there is no number written, the coefficient is $1$. In the term $x$, the coefficient is $1$.
Which part matters: We must be careful about which part we're finding the coefficient of. In $4ab$, the coefficient of $b$ is $4a$.
Fractions: Coefficients can be fractions. In $\dfrac{2a}{3}$ or $\dfrac{2}{3}a$, the coefficient of $a$ is $\dfrac{2}{3}$.
Independent Apply Task
Complete all questions on the worksheet showing all working out.