Lesson 25: Small friend plus 4 on an abacus
Level 3, Small Friends Pond. When there are not enough beads, a friend helps.
What your child does, card by card
Small friends: plus 4. 3 + 4. Where do 4 more beads go? PlayBuddy opens the lesson: “I want to add four, but there are not enough beads.”
4 and 1 make 5: the top bead is 5. So it is 4, and 1 more. The abacus makes 4 and 3, then clears. Here the hands lead: they show 4 and 5, and a moment later the beads copy each one. The labels “4 and 1 make 5” and “3 and 2 make 5” light up as each idea comes. “You found the friends of 5 last time.” Any bead or finger may be tapped afterwards.
Find the friend: the beads show 4 and 3 in turn and hold still, and your child shows each one's friend on the drawn fingers, so 4 and 1 and 3 and 2 each make 5.
3 + 1, then 3 + 4: 3 + 1: one bead is free. Push it! A yellow line goes round the bottom beads as the kids name them. 3 appears on the beads, then the rod clears again. Each label lights in turn: “3 + 1: 1 bead free” and “3 + 4: only 1 free”. After the show, the child can touch: “3 + 4: only 1 bead is free. Not enough!”
Count four more: 3, then 4, 5, 6, 7. The abacus makes 3, then clears. “4”, “5”, “6” and “7” glow on the card in step with the beads. The card ends on a touch: “It works. But it is slow.”
Add 5, take 1 back: 5 is 4 and 1. So 5 is 1 too many. The beads show 3 and go back to zero. Here the hands lead: they show 3, 8 and 7, and a moment later the beads copy each one. Above, “+5: the top bead”, “1 too many: 1 bead back” and “7” take turns to glow. Its words: “7 again! The same as counting.”
Plus 4: add 5, take 1 back: top bead down. The friend, 1, goes off the bar. The beads act out the friend rule while “+5: the top bead”, “−1: the friend” and “+4 = +5 −1” light up; then your child must work out 3 + 4 and 2 + 4, a green ring on each bead in the friend's order.
In Try it a green ring marks the next bead while your child works out 1 + 4, 4 + 4 and 2 + 4.
The tiny practice drops the ring: work out 3 + 4, 0 + 4, 2 + 4, 5 + 4 and 4 + 4, each round starting from its own number.
In Copy me the drawn hand holds up 7, 5 and 8 in turn, and your child copies each one in beads.
Then the beads hide and the sums 1 + 4, 3 + 4 and 4 + 4 are done in the head, the answer shown on the fingers.
You're ready! Not enough beads for 4? Add 5, take 1 back.
What this lesson trains
18 answers in about five minutes. The tasks take 23 bead moves in all: 11 with a top bead and 12 with bottom beads. The biggest number is 9, all on the ones rod; the 2 rods to its left stay clear and are named on a touch. Then 3 quick looks in your head. Small friends do 8 of the 10 sums, by +4 = +5 −1.
Your child’s first moves: work out 1 + 4, 4 + 4 and 2 + 4.
Fingers and hands
In the lower window two drawn hands work as a finger abacus and always match the beads: a finger up is a bottom bead (1), the thumb out is the top bead (5), a closed hand is zero. In this lesson the hands show zero and 1, 2, 3, 4, 5, 6, 7, 8 and 9.
+4 on the fingers: the thumb opens and one finger closes (+5 −1).
On “4 and 1 make 5” the hands move first and the beads follow, so your child sees that a finger and a bead move together: open a finger and a bead goes to the bar, close it and the bead goes back.
Copy me turns it round: 7, 5 and 8 appear on the hand first.
What PlayBuddy and PlayType say
PlayBuddy: “I want to add four, but there are not enough beads.”
PlayBuddy: “Four and one are friends. Three and two are friends.”
PlayBuddy: “To add, push beads to the bar.”
PlayType: “Let's count four more. Four, five, six, seven!”
PlayBuddy: “Five is one too many. So one bead goes back!”
Stars
Three stars for up to 1 slip in 18 answers, two stars for up to 4. A number counts as a slip only when it stays wrong for a moment and is not on the way to the answer, so a child who moves beads one at a time is never marked down. After two slips on one task the green ring comes back.
About Small Friends Pond
Small Friends Pond is Level 3 of nine (grade 1 to 2): +4 +3 +2 +1 and −4 −3 −2 −1 with the top bead and a small friend. In your head: small friend sums in your head.