Grade 10 · Core Mathematics · Lesson 2 of 14

Four Products on a Noticeboard

A Grade 10 Core Mathematics CBE lesson from the sub-strand Quadratic Expressions and Equations. In it, learners map four products from two binomials.

Strand Numbers and AlgebraSub-strand Quadratic Expressions and EquationsLesson code 10CM-13-L240 minutes · 3 slides

KICD learning outcome (a)

Form quadratic expressions from different situations.

By the end of this lesson, learners should be able to

Map four products from two binomials.
Collect like terms with clear notation.
Verify an area expression by substitution.

Key vocabulary

Binomial: An algebraic expression made from two terms joined by addition or subtraction.; The side p+19 is a binomial with variable and constant terms.
Coefficient: A numerical factor multiplying a variable or its power.; In 46p, the coefficient of p is 46.
Verification: A check that two equivalent representations give the same result.; At p=2, compare 21×29 with 4+92+513.

Lesson preview

Slide 1 · Map the noticeboardOpening · 10 min

Figure 1: A rectangular noticeboard partitioned into four regions, with the area of each calculated by multiplying its side lengths.

A noticeboard with symbolic length and width can be partitioned into four regions. Each region records one multiplication, so the complete area is the sum of four products.

Label the sides p+19 and p+27.
Pair each term from one side with each term from the other.
Keep p², p-terms, and constants distinct.
Use centimetres squared for the area.

Worked example. p×p gives p². p×27 gives 27p and 19×p gives 19p. 19×27 gives 513. Answer: The regions are p², 27p, 19p, and 513..

Check question: When finding the four area regions for a noticeboard with side lengths $p + 19$ and $p + 27$ , which multiplication gives the constant region?

$19 \times 27$
$p \times 27$
$p \times p$
$19 \times p$

Show answer

$19 \times 27$ . The constant region is formed by multiplying the two fixed number lengths together, which is $19 \times 27 = 513$ .

Slide 2 · Collect the middle termsModel · 18 min

Figure 2: A flowchart demonstrating how the four area products are combined into a simplified polynomial by adding the like terms.

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

All 3 slides with diagrams and class activities
Teacher notes, SNE adaptations and assessment checks
Homework and the other 13 lessons in this sub-strand

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