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Episode 3 · Stories from Ganita House

Rows in the Garden

Growing patternsPrediction

Tata plants rows of seedlings behind Ganita House: 3, then 5, then 7, then 9. Mihir predicts the next row before a single plant goes in, and then they plant it and count every one.

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Read the story

The same story, told as a comic. Read it together, slowly.

The Ganita house, with its wooden name board1
In a big, happy house called Ganita, there lived a girl who loved numbers. Her name was Chitra.
Tata, Chitra and Mihir at the bare garden patch, with a basket of seedlings2
Behind the house, the garden patch was bare, and Tata had a basket of seedlings.
TataSeedlings today, kanda. Five rows for the new patch, and every row different.
MihirHow many in each row, Tata?
TataThe rows will tell you, if you count them as they go in.
ChitraThen I count every row. Out loud, so nobody has to guess.
The garden patch with the first row of three seedlings planted3
The first row went in, and Chitra counted it out loud.
ChitraRow one. One, two, three.
MihirThree in row one!
The garden patch with three rows planted, of three, five and seven seedlings4
Row two held five, two more than row one. Then row three went in.
ChitraRow three. One, two, three, four, five, six, seven.
MihirSeven! Two more again!
The garden patch with four rows planted, of three, five, seven and nine seedlings, and the fifth line still empty5
Row four held nine. Tata counted it slowly, and he counted it twice. One row was left, and its line was still empty.
ChitraThree, five, seven, nine. Every row grows by two. Exactly two.
MihirEleven! Nine and two more is eleven!
ChitraThat is the pattern's answer. Now the row has to agree. Plant it, and count.
The finished garden patch, five rows of three, five, seven, nine and eleven seedlings6
They planted the last row and counted every plant as it went in: eleven, exactly eleven. The row agreed with the pattern.
ChitraNow the whole patch. Three and five is eight. And seven is fifteen. And nine is twenty-four. And eleven is thirty-five.
TataThirty-five seedlings, standing in their rows.
ChitraProven.

Try the math

Plant a row, then predict

0 of 5 rows planted · 0 seedlings

Your Turn

Tata plants a new patch where the rows grow by three instead of two: 4, then 7, then 10. How many seedlings does the fourth row need, and how many are in the whole patch?

Off-screen activity

At home: make rows of buttons, spoons or stones: 3, then 5, then 7, then 9. Ask your child how many the next row needs, then build it together and count. Was the prediction right?

Chitra

For parents

Today's idea was a pattern that grows by the same step. The garden rows held 3, 5, 7, 9 and 11 seedlings, each row two more than the row before. Mihir predicted 11 for the last row from the rule, then proved it by planting the row and counting every plant.

Ask at dinner: what in our house grows by the same amount every time, and what would come next?