Vectors – Grade 11 math lesson

Lesson 3 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 can vectors show that two lines are parallel?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Going the wrong way along a vector. Going backwards along a makes it −a.
Adding the magnitudes instead of the vectors. Add the components, then find the length.

Tip for home: Talk about wind and boat speeds: two vectors combining.

What your child will learn

Learning goal: add, subtract and multiply vectors and use them to describe paths and prove results.

Success looks like

I can add and subtract vectors.
I can find the magnitude of a vector.
I can use vectors to describe paths.

Key words

vector: a quantity with size and direction
magnitude: the length of a vector
scalar: a number that multiplies a vector
resultant: the vector you get by adding vectors

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Give directions as vectors on a grid to move a counter to a target.

The big ideas (for the adult)

A vector has a size and a direction. A column vector shows how far across and how far up or down.

Add vectors by adding their components; a vector multiplied by a number keeps its direction but changes its length.

To find a path between two points, go via points you know: AB = AO + OB. Parallel vectors are multiples of each other.

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 HSN.VM.B.4.b: “Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.”

Common Core State Standards HSN.VM.A.1: “(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).”

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