Iteration – Grade 11 math lesson

Lesson 9 of 23 in the Grade 11 math course

US version. US grades, US spelling and dollars ($). · UK Maths Department

A complete 45-minute lesson for grade 11 (ages 16–17) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.

Time: 45 minutes + 20 min homework
Grade: Grade 11 (ages 16–17)
You need: Paper, a pencil and this page
Graded: Instantly, with explanations

For parents: how to use this lesson

You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.

Read what your child will learn and the big ideas together.
Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
Finish with the exit ticket and the talk question: “How do you know when to stop iterating?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Using the first answer each time instead of the latest one. Use the ANS key: feed each answer back in.
Rounding too early. Keep full calculator values until the end.

Tip for home: Try repeatedly pressing √ on a calculator: what number does it settle on?

What your child will learn

Learning goal: find approximate solutions using iteration and sign changes.

Success looks like

I can show a solution lies between two values.
I can use an iteration formula.
I can give a solution to a stated accuracy.

Key words

iteration: repeating a process using the last answer
sign change: from negative to positive or back
approximate: close but not exact
converge: settle towards one value

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Use the ANS key on a calculator to repeat an iteration formula and watch the values settle.

The big ideas (for the adult)

Some equations cannot be solved exactly, but we can get as close as we like.

A sign change: if f(1) is negative and f(2) is positive, there is a solution between 1 and 2.

Iteration uses a formula such as xₙ₊₁ = ∛(5 − xₙ) again and again; each answer is fed back in until the values settle.

The lesson, step by step

45 minutes in 5 parts
Part	Time	How it is checked
Starter: quick recall	5 min	Graded by Classfern
Teaching input	10 min	Not assessed, self-checked
Worked examples and guided practice	9 min	Not assessed, graded by Classfern
Independent practice	15 min	Graded by Classfern
Closure and exit ticket	6 min	Graded by Classfern, self-checked

Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.

The lesson

It runs here on the page. No sign-up and no names – progress is kept only in this browser.

Homework and practice at home

20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.

More practice

All Grade 11 math lessons and tests · Math Department

Curriculum

Common Core State Standards HSA.REI.D.11: “Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*”

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