It was rather sheepishly I showed a friend what my eight year old and six year old had been doing in maths over the past month or so. I could see the incredulity in her eyes. ‘Your daughter is only just learning what 3 plus 4 is?’ I could hear her silent thoughts. And I doubted myself just a little. But I didn’t stop what I was doing. No, there was something deep inside me which yelled out that this was the right way to teach my younger girls maths, and I just needed to keep on keeping on.

As we approach the end of the first of the Life of Fred maths books ‘Apples’ I can honestly say I am so pleased I didn’t give up. These books are gems and my girls adore maths right now, often asking for more than one lesson per day. They love the story of Fred, they really enjoy putting together their maths notebooks, and I can see they are learning heaps. But they are not just learning, they are understanding and applying their maths to every day situations.

It has taken just over two months to complete Apples and, having looked at what each girl would have learnt in their regular maths program, I can say with confidence that we have covered far more. And because I am the one doing the teaching, I know exactly what they know and more importantly what they understand. I LOVE this type of teaching. It may be more work but I am excited about what each day brings.

Any how, here is the enormous amount of learning which has gone on in the last four weeks or so, along with our maths notebooks.

**Time {hours}**: I do this very simply. I have precut lots of clocks which the girls use one of each lesson, add the time mentioned in*Apples*and stick it in their note book. Simple right? The best thing though has been watching my six year old moving the hands of our learning clock and working out on her own the times displayed on the various clocks around our house, having never shown any interest in time prior to this:Right at the end of the book, Fred learns how to tell the time in 5 minute increments. This not only showed the girls how useful knowing their five times tables was, it also helped B6 to understand how a clock works. I went through very slowly with her about seconds, minutes and hours. We had already covered this in her computer based curriculum the previous year, but they had figured more on rote learning of o’clock, quarter past and half past. She had never really understood. Now she understood much better. This was revision for A8, so I had her play teacher to give B6 more practice at times. I made the promise that as soon as they could both tell the time, Daddy and I would buy them a wrist watch 🙂**Days of the week:**Again I do this very simply. Each day we run through the days in order, figure out today’s day and the girls write it down in their note books. I have a book mark containing all the days to help with spelling, but we don’t really need that anymore: The girls also made a flap mini book detailing the days of the week and the order in which they come, with their ordinal number**Months of the year:**In the same vein, we go through all the months of the year each day, and the girls write down the date and month next to the day in their note books (again they use the bookmark of the months of the year to help with spelling): I also made a months of the year flap mini book with ordinal numbers underneath each flap:**Addition sentence {Addend plus Addend equals Sum}**: Apples focuses on addends of seven. At first I didn’t understand the importance of focusing on just one set of addition facts but I absolutely see it now. First I created an addend plus addend equals sum mini book: The girls quickly learnt that it does not matter what order the addition is done in (2+5=7 just like 5+2=7). This is called the Identity quality of addition {Order does not matter}. I made a mini*Properties of Addition*booklet for the girls to fill in as we go along: We did lots and lots of addition practice focusing only on the addends of seven. This led the girls to fully understand the rather arbitrary 2x + 5x = 7x, which was necessary to understand to begin algebra: And lastly they did some addition colouring in:**Shapes {Circles, Ellipses, Triangle and Square}:**We did all sorts of activities linked to shapes. The girls pasted a sheet of shape properties: We looked for specific items around the house which were certain shapes and made shapes on their elastic band peg boards: The girls also divided the shapes into sets:

Next we stole Lillie to help us play ball and make up different shape configurations whilst we played. This was a ‘game’ Fred ‘plays’ with the seven bored monkeys he comes up against. He was the ball. We used an actual ball rather than a child and had great fun!

**Counting by fives:**We basically learned to skip count, which A8 could do easily and B6 could do mostly. I had them paste the five times table in their book and they labeled a thermometer with increments of five:As mentioned above. we also revised time in increments of five.**Introduce the idea of negative numbers:**Apples introduces the negative numbers as the temperatures below zero. I could see this was hard for my youngest to grasp. I printed out a blank thermometer, and the girls added the values, counting down by fives until they reached zero and continuing down into the negative numbers (see picture above). I also printed three small thermometers and the girls read a thermometer in the air, in the fridge and in the freezer, recording their work: This was only introducing the idea that negative numbers exist, so I wasn’t too worried that B6 didn’t really understand.**Counting by tens:**We did this verbally. Both girls knew their tens tables.**Time {AM and PM}:****Large Numbers:**{A million as a large number; a vigintillion as an even bigger number}:**Sets:**we used the following book to learn all about sets and made up some simple sets using M’n’ms and Revels as counters:

I had the girls complete some notebook pages about sets where they divided stickers into sets of the same kind (vehicles with wheel and vehicles without):**Left and right hand side:****The concept of zero**: There are lots and lots of activities out there for this particular book, and I may do some of them later on, but for now this was a simple introduction about zero and its many properties. The girls made up a huge zero from construction paper and pasted a whole heap of different words, all of which meant zero:**Horizontal and vertical lines**:**Greater than, less than and equal to**: We had a lot of fun with this one! I found some very cute printables of a crocodile with his mouth wide open. As he always faces towards the largest amount it is easy for the girls to recognise ‘greater than >’ and ‘less than <‘. We spent a long time playing with lots of blueberries and the three signs: How cute are they?**Introducing fractions with 1/6**:**Measuring in feet and inches**: One thing I want to collect for the girls’ notebooks is lots of maths tools and manipulatives. To this end, I printed out a rule using this print out. The girls then went around the house measuring everything in sight, including each other:**Equal and Not Equal**: The girls made a note page to illustrate the simple concepts of equal to and not equal to: And we played the ‘not equal’ game where we all took it in turns to list off lots of things that are not equal!

### Maths Games Played

Any time I had been remiss and forgotten to plan any activities for the next day, I brought out one of our many maths themed board games. The girls both had fun making addition and subtraction puzzles. For A8 this was revision and child’s play but for B5 it was a defining moment, because it was whilst doing the number sentences for 7 (1+6=7, 2+5=7, 3+4=7 etc) that she noticed a pattern. She then began to naturally group the puzzles into the patterns which made sense to her (2+5=7, 5+2=7, 7-2=5, 7-5=2). Obviously these aren’t hard sums, and they were the sums she had been learning. No, I wasn’t impressed because of the trickiness of them, I was impressed because she had noticed the patterns by herself, and then she applied that knowledge to sums she didn’t know, grouping for example the number bonds of ten together, of nine together….Another time she focus on the addend ten, taking away numbers from it. Again enjoying the patterns she found. She played with this for hours and I could see just how vital playing is for a child to make those all important connections.

Another game Lillie played with them one afternoon was number bingo:

I wasn’t here to watch this but all three girls seemed to have had a good time 🙂

I also created a shop in which everything cost the all the addends of seven:

And the girls even played a naming shapes in Spanish game!

### Apples: Mathematical Exploration – Archimedes

Each Life of Fred book we use I will be keeping my eyes open for something the girls can dig a bit deeper into, thus enriching their mathematical experience. For Apples, I chose to explore the theories of Archimedes. The girls learnt all about this well known mathematician, as well as figuring out how to measure large quantities of something, and also about why Fred’s boat floated and then sunk (displacement theory). I will be writing a separate post for this:

We also did a huge maths investigation into polygonal stars using Penrose, the mathematical cat, at our starting point. Again I will be writing a separate post about this.

### Checking the Girls Knowledge

I made a pdf of the scope and sequence of Life of Fred apples and used this to check the girls understood everything after we finished the book. Anything they were a bit rusty on we revised until they knew it without thinking about it.

To double check I had them fill in these free worksheets based on the Apples book.

I love this! My kids really liked Life of Fred in the beginning, but burned out on it during the fractions book. However, I think I am going to try and pick it up again. You are an amazing teacher!

Blessings, Dawn

Thanks Dawn. You know what they say…when mama’s happy, everyone’s happy…and Life of Fred is FUN!

Wow! You sure have covered a lot! I have heard wonderful things about Life of Fred books.

They are good, and very funny. It is definitely a peculiar way to study maths. Peculiar but fun 🙂

That is one impressive math program you’ve made. I love the notebook idea. I’m going to have to borrow some of these activities!

Thanks Blair. The handy dandy thing about the maths journals is that the girls pick them up and look through them fairly frequently, which they never did with their maths text books or online program.

Wow. I think I need to go back to Apples and do it again using some of your ideas. You really fleshed out the lessons and made it so much fun and hands-on! Thanks for these inspiring posts!

I really wanted to use Life of Fred with Princess because it fits how she learns perfectly, but she couldn’t stand the idea of using a different program than her brothers.