Upper and lower bounds – Grade 9 math lesson

Lesson 3 of 17 in the Grade 9 math course

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

A complete 45-minute lesson for grade 9 (ages 14–15) 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 9 (ages 14–15)
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: “Why does the error interval use < at the top and ≤ at the bottom?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Using the wrong half unit (7.4 to 1 d.p. as 7.3 to 7.5). Half of one tenth is 0.05.
Using the upper bound for both numbers in a division. Big answer: big ÷ small.

Tip for home: Talk about rounded figures in the news: what could the real number be?

What your child will learn

Learning goal: find upper and lower bounds and write error intervals.

Success looks like

I can find upper and lower bounds.
I can write an error interval.
I can use bounds in calculations.

Key words

upper bound: the largest value that rounds to the number
lower bound: the smallest value that rounds to the number
error interval: the range of possible values
truncate: cut off digits without rounding

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Measure a length to the nearest centimeter and talk about what the real length could be.

The big ideas (for the adult)

A rounded number could have been anything within half a unit either side. 7.4 to 1 decimal place is between 7.35 and 7.45.

Write this as an error interval: 7.35 ≤ x < 7.45. The upper bound itself would round up, so it uses <.

In calculations, choose the bounds that give the largest or smallest answer: for a maximum quotient, divide the upper bound by the lower bound.

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 9 math lessons and tests · Math Department

More Grade 9 math lessons

Curriculum

Common Core State Standards HSN.Q.A.3: “Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.”

Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.