Curriculum by subject

Mathematics: Waldorf-inspired blocks for Grades 1 and 3

Selemo's mathematics starts with the whole and moves to the parts, and with movement before pencil. Numbers are walked, clapped and found in the world before they are written down.

Level Grades 1 and 3 (Foundation Phase)
Blocks 2
Weeks of lessons 7
Outcomes 25

In Grade 1 the numbers are met as qualities and the four operations arrive together as four friends at a market. In Grade 3 mathematics turns practical: body measures, metres and litres, rand coins, the clock and a shelter built to size.

The blocks

Grade 1, 4 weeks, 4 days a week, about 100 minutes a day

The Quality of Numbers and the Four Market Friends

A four week Grade 1 mathematics block. In the first two weeks the numbers one to twelve are met as qualities in stories, in the world and in the body, with Roman and Arabic numerals. In the last two weeks four friends at a Lowveld street market bring adding, taking away, multiplying and sharing to life, working from the whole to the parts with beans, stones and rhythm.

Why this block

Meeting each number first as a quality (the one sun, the pair, the three-legged pot, the open hand) gives a child living pictures to stand on before any sum is written.
The Roman numerals grow straight out of the fingers and hands, so writing numbers begins in the body and the child can always find a number again.
The four market friends turn adding, taking away, multiplying and sharing into people the child knows and likes, so each operation has a face, a gesture and a sign.
Working from the whole to the parts lets a child find many right answers and keeps every part tied to the whole it came from.

At six and seven children love rhythm, counting games and stories, and are ready to find numbers in their own hands and in the world around them. The block can come at any time of the Grade 1 year, often after the first letters block. Its stories move through the South African seasons, so it fits any term.

The weeks

Week 1: One to six
Week 2: Seven to twelve
Week 3: Ayanda gathers and Mme Dineo gives away
Week 4: Oom Danie brings many and Kokwana Tsakani shares

Grade 3, 3 weeks, 4 days a week, about 100 minutes a day

Measuring and Building

Three weeks of practical mathematics. Your child measures with hand spans, feet and strides, discovers why people agreed on shared measures, works with metres, litres, kilograms, money and time in real tasks, and ends by planning, building and reporting on a shelter or model house, after meeting homes from across South Africa.

Why this block

Measuring makes sense when it is needed for something real, like a shelf, a loaf of bread or a shelter.
Starting with the body and moving to the metre lets your child discover for themselves why people agreed on shared measures.
Homes across South Africa show how people build wisely with what their land gives them.
The measured drawings, written instructions and building report leave clear evidence of learning for a Foundation Phase assessment.

At about eight or nine, children want to know how things are made and to do real work themselves. Autumn and spring bring dry, mild days for measuring the garden, drying mud bricks and building outside.

The weeks

Week 1: Measuring with the body
Week 2: Metres, litres, kilograms, money and time
Week 3: Homes and shelters

What a morning looks like

A real day from Measuring and Building: The metre comes home.

10 minin-breath
Opening: Morning verse
Light the candle and say the morning verse together with the movements.
15 minout-breath
Rhythmic work: Ten tens make a hundred
Lay the tape measure along the floor. Walk beside it, stepping on every 10 cm and counting in tens to 100, then back to 0. Say together: Ten tens make a hundred, a hundred centimetres make a metre. Then say Heel to Toe with the movements, and step the two times table once more.
15 minin-breath
Recall: Remember the metre
Ask your child to tell what Delambre and Méchain did, and why the scientists wanted a measure taken from the Earth. Ask what grandparents measured with before metres. Then look at the tape measure together. Find 1 m, then 50 cm and 10 cm.
35 minout-breath
The new story: Measuring the garden
Your child makes a metre rope with a knot every 10 cm. Go outside and choose three lengths, such as a bed, a wall and a path. For each one, your child guesses in metres and writes the guess down, then measures with the rope, counting whole metres and using the knots for what is left. Check each with the tape measure. Do not correct the guesses; ask whether each guess was more or less.
20 minin-breath
Main lesson book: A measured map
In the main lesson book, your child draws the garden from above, as a bird would see it, using a ruler for straight edges, and writes each measured length along its line. Under the map, they rule a table with three columns: what we measured, my guess, the measurement. Ask which guess was closest.
5 minin-breath
Closing: Closing
Hang the metre rope next to the family measuring stick. Blow out the candle together.

The evening before

Get 2 m of string, a tape measure, a clipboard, paper and a sunhat. 5 minutes
Walk the garden or yard and remove anything sharp. Choose three lengths to measure. 10 minutes

The account of the metre is recalled, your child makes a metre rope and measures the garden in metres, guessing first, and draws a measured map. The whole morning runs about 100 minutes.

Materials to have at hand

Main lesson book
Block crayons
A candle and matches, for the adult
Counting basket of dried beans
Smooth stones and shells
Straight sticks or twigs
Flat stones for the times-table walk
Small saucers, cups or bowls
Small dolls, stones or pine cones to be the people sharing
A cloth to work on

What you will notice

The signs Selemo asks you to look for as the block goes on. Each one belongs to an outcome; when you see it, a sentence in the journal is enough.

Language and story

Tells beginning
middle and end
Uses words from the story
Speaks a whole verse alone
Tells how the builder solved the problem in their own words
Names the materials and the order of the work

Number

Finds examples of a number in nature or at home
Counts in fives while clapping
Counts back from twenty
Writes the numeral for a counted set
Shares twelve beans into equal groups and says what happened
Finds two numbers that make twelve in more than one way
Measures a table in hand spans and compares with a friend
Measures to the nearest centimetre
Estimates before weighing and compares
Adds the cost of three items on a list
Writes the estimate and the measured result side by side
Says whether the estimate was more or less than the result
Writes 135 cm as 1 m 35 cm and back again
Knows that 1 kg is 1000 g when weighing flour
Lays VII or IX with sticks and says the number
Shows V with an open hand without being reminded
Names the friend who gathers
gives away
brings many of the same or shares
Draws the sign that belongs to each friend
Deals beans one at a time into groups until none are left
Says twelve shared by three is four each

Movement and music

Keeps a steady beat across a whole verse

Practical life

Draws a plan before building
Uses measures in the plan
Names two building materials and where they come from
Carries, uses and puts away tools safely
Weighs and measures ingredients for a recipe without help

Literacy

Writes instructions someone else can follow
Finds a measurement in a short text

Science and nature

Tests which material holds the most weight

Arts and handwork

Keeps the model in proportion to the plan

Where the timing differs from CAPS

Selemo meets most CAPS topics in its own order. These notes say where it comes earlier or later. They are written in Selemo's own words and are being checked against the Department of Basic Education's documents.

Experiences the qualities of numbers one to twelve (one is whole, two is a pair, three a triangle) in stories and the world.

Selemo meets numbers as qualities first (one as a whole, two as a pair) before quantities and symbols; CAPS starts from counting and number symbols.

Counts forward and backward to one hundred in rhythm, and in twos, threes and fives.

Selemo counts to one hundred in rhythm early in Grade 1, ahead of the smaller first-term range in CAPS.

Counts forward and backward to one hundred in rhythm, and in twos, threes and fives.

Selemo counts in threes as well as twos and fives, walked and clapped as the start of the times tables.

Writes Roman and Arabic numerals to twelve and numbers to one hundred.

Roman numerals are a Selemo addition (drawn from straight lines) and are not part of CAPS Grade 1.

Understands the four operations as stories with concrete objects, working from the whole to the parts.

Selemo brings all four operations in together in Grade 1, starting from the whole and its parts; CAPS builds from adding and taking away.

Understands the four operations as stories with concrete objects, working from the whole to the parts.

Selemo names multiplication and division as operations in Grade 1 and begins walking the times tables; CAPS keeps to grouping and sharing with objects at this stage.

Safety notes

Dried beans and small stones are a choking risk for babies and toddlers in the house. Count them back into the basket at the end of every lesson.
On the number hunts, look closely at bees, wasps and spiders from a little way off and do not touch them.
The adult does all cutting with a saw, secateurs or a craft knife. Your child uses child-safe scissors.
Stay close whenever there is water in a basin or bucket, and empty it as soon as you finish.

Teach it at home

Selemo plans these blocks into your year, prepares each evening with you, and keeps the record as you go.

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