Mix Mountain — Lesson 67a: Long sums with friends

What your child does, card by card

Long sums with friends. 25 + 37: tens first, then ones. PlayBuddy opens the lesson: “Big numbers have tens and ones. Let's add both.”

23 + 51 = 74: add 5 tens. Then add 1 one. Yellow marks the tens rod and the ones rod while the kids talk about them. The abacus makes 23, then clears. Here the hands lead: they show 23, 73 and 74, and a moment later the beads copy each one. On the card, “Start at 23”, “+ 5 tens = 73” and “+ 1 one = 74” light up one by one. Then the card invites a touch: “No friend needed here.”

25 + 37: add 3 tens: 2 tens and 3 tens: a small friend. The tens rod is outlined in yellow while the kids explain. The beads show 25 and go back to zero. Here the hands lead: they show 25, 75 and 55, and a moment later the beads copy each one. Each label lights in turn: “Start at 25” and “+ 3 tens = 55”. After the show, the child can touch: “Top bead down, two tens off.”

Then add 7 ones: 5 and 7: the mix of lesson 60. A yellow line goes round the ones rod as the kids name it. 55 appears on the beads, then the rod clears again. Here the hands lead: they show 57, 52 and 62, and a moment later the beads copy each one. “+2”, “−5” and “+10 = 62” glow on the card in step with the beads. The card ends on a touch: “2 up, top bead off, one ten on.”

First a reminder (“62 − 38”): the beads build 62, 12, 32, 22 and 24, ring by ring, while your child watches. Take 3 tens: the small friend. Then 8 ones: one ten off, 2 on.

Try it: your child works out 25 + 37, 56 + 28, 62 - 38 and 84 - 28, with a green ring on the next bead to move.

Then a short practice without rings: work out 34 + 28, 47 + 36, 71 - 45, 18 + 65 and 90 - 54, each round starting from its own number.

In Copy me the drawn hand holds up 62, 84 and 24 in turn, and your child copies each one in beads.

In your head: the abacus is covered and your child works out 25 + 37, 56 + 28 and 62 - 38, showing each answer on the drawn fingers.

You're ready! Tens first, then ones. Each rod gets the friend it needs.

What this lesson trains

About five minutes and 15 answers. Altogether the child makes 46 bead moves (16 with the top bead, 30 with bottom beads). Up to 90, read and set from the left. Then 3 quick looks in your head. 9 of the 9 sums need a friend (“+3 = +5 −2”, “+7 = +2 −5 +10”, “+8 = +3 −5 +10”, “−3 = −5 +2”, “−8 = −10 +2”, “−8 = −10 +5 −3”, “+2 = +5 −3”, “+8 = −2 +10”, “+6 = +1 −5 +10”, “−4 = −5 +1”, “−5 = −10 +5”, “+5 = −5 +10” and “−4 = −10 +6”); the others use free beads.

The first thing your child does: work out 25 + 37, 56 + 28, 62 - 38 and 84 - 28.

Fingers and hands

Below the abacus the drawn hands show zero and 18, 23, 24, 25, 26, 34, 36, 47, 52, 55, 56, 57, 62, 71, 73, 74, 75, 83, 84 and 90 here, finger for bead: the left hand counts the tens, the right hand the ones.

+3 on the fingers: the thumb opens and 2 fingers close (+5 −2). −3 on the fingers: the thumb closes and 2 fingers open (−5 +2). +2 on the fingers: the thumb opens and 3 fingers close (+5 −3). −4 on the fingers: the thumb closes and one finger opens (−5 +1).

+7 on the fingers: the right hand opens 2 fingers and folds the thumb, then the left hand opens one more finger for the ten (+2 −5 +10). +8 on the fingers: the right hand opens 3 fingers and folds the thumb, then the left hand opens one more finger for the ten (+3 −5 +10). −8 on the fingers: the left hand closes one finger for the ten and the right hand shows 2 more (−10 +2). −8 on the fingers: the left hand closes one finger for the ten, then the right hand puts the thumb out and closes 3 fingers (−10 +5 −3). +8 on the fingers: the right hand lets 2 go and the left hand opens one more finger for the ten (−2 +10). +6 on the fingers: the right hand opens one finger and folds the thumb, then the left hand opens one more finger for the ten (+1 −5 +10). −5 on the fingers: the left hand closes one finger for the ten and the right hand shows 5 more (−10 +5). +5 on the fingers: the right hand lets 5 go and the left hand opens one more finger for the ten (−5 +10). −4 on the fingers: the left hand closes one finger for the ten and the right hand shows 6 more (−10 +6).

On “Long sums with friends” 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.

The fingers lead in Copy me (62, 84 and 24); the beads answer.

What PlayBuddy and PlayType say

PlayBuddy: “Big numbers have tens and ones. Let's add both.”

PlayBuddy: “Top bead down, small friend off.”

PlayType: “Now take away tens and ones. Tens go first.”

Stars

With 1 or fewer slips across the 15 answers your child earns three stars; 3 or fewer, two.