Bridging lesson
Basic Algebra
Batayang Algebra
Evaluate expressions, combine like terms, solve linear equations and substitute into formulas.
About 25 minutes
Why it matters in Grade 11
Sequences and series use formulas such as $a_n=a_1+(n-1)d$ and $S_n=\frac{n}{2}(a_1+a_n)$; Functions and Their Graphs evaluate $f(x)$ for many inputs; Trigonometry rearranges $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$; and every finance formula in Term 3 is substitution into $F=P(1+i)^n$ and its relatives.
Needed directly for: Patterns, Sequences and Series (Term 1, Weeks 3–4), Functions and Their Graphs (Term 1, Weeks 9–10), Trigonometry of Triangles (Term 2, Weeks 3–4)
Later topics that build on these: Sequences in Finance, Piecewise Functions, Compound Interest, Annuities and Cash Flows, Business and Consumer Loans, Correlation and Line of Best Fit.
Lesson
Letters stand for numbers
Explain$3x$ means $3\times x$. To evaluate $3x+5$ at $x=4$, replace $x$ with $(4)$: $3(4)+5=17$. Always substitute negative numbers inside parentheses: $x^2-2x$ at $x=-3$ is $(-3)^2-2(-3)=9+6=15$.
Like terms and the distributive property
Explain- Like terms share the same variable part: $5x^2$ and $-2x^2$ are like terms; $5x^2$ and $5x$ are not.
- Distribute to every term inside: $3(x+2)=3x+6$.
- $3(x+2)-x=3x+6-x=2x+6$.
Solving linear equations: undo in reverse order
ExplainWhatever is done to one side must be done to the other. Undo addition and subtraction first, then multiplication and division.
- $x+7=12\Rightarrow x=5$ (subtract 7).
- $4x=28\Rightarrow x=7$ (divide by 4).
- $2x-3=11\Rightarrow 2x=14\Rightarrow x=7$.
- $\frac{x}{3}+1=5\Rightarrow \frac{x}{3}=4\Rightarrow x=12$.
- $5(x-2)=3x+4\Rightarrow 5x-10=3x+4\Rightarrow 2x=14\Rightarrow x=7$.
Formulas are equations with several letters
ElaborateSimple interest: $I=Prt$. With $P=5000$, $r=0.03$ (3%) and $t=2$: $I=5000\times0.03\times2=₱300$. Rates go into formulas as decimals. To find a missing letter, substitute what you know and solve: $V=\frac{1}{3}Bh$ with $V=60$ and $B=12$ gives $60=4h$, so $h=15$.
Worked example: a tricycle fare
ElaborateA ride costs ₱15 plus ₱2 per kilometre. A passenger paid ₱35. Let $k$ be the distance: $15+2k=35$. Subtract 15: $2k=20$. Divide by 2: $k=10$ km. Check: $15+2(10)=35$. ✓
Common errors to watch for
Evaluate- Reading $3x$ at $x=4$ as 34.
- Distributing to only the first term: $3(x+2)\ne3x+2$.
- Dividing one term instead of the whole side.
- Using $r=3$ for a 3% rate.
- Forgetting parentheses when substituting a negative number.
Check yourself
Three quick items with instant feedback. Answer, then press Check.
Ready? Retake the Basic Algebra placement test (13 items) to confirm the skill.
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