Golden Bead Multiplication

Materials

• Golden bead material or base-ten blocks — plenty of pieces, since the same number is laid out several times
• Large number cards (several small sets if you have them, one per layout, plus cards for the answer)
• A work mat, a tray, and a "bank" dish
• Paper and pencil to record the finished problem

No materials at home? Use the virtual Golden Beads & Mat.

Before this lesson

• Golden Bead Addition

Aims

Presentation

1. 1 Start with a problem where no column overflows, such as 1,212 × 3. Tell your child the plan before you begin.We are going to take one thousand two hundred twelve — three times!
2. 2 Have your child build 1,212 on the mat and check it. Then build it again below, and check. Then a third time.That is once… twice… three times. The same number every time.
3. 3 Pause and look. Ask what your child notices about the three layouts.Every row is exactly the same. When we add the same number again and again, we call it multiplication.
4. 4 Push all three layouts together column by column, starting with the units, and count each column aloud: six units, three tens, six hundreds, three thousands. Read the product — 3,636 — stack the answer cards, and record the problem on paper.One thousand two hundred twelve taken three times makes three thousand six hundred thirty-six.
5. 5 Another day — or right away, if your child is eager — present 1,568 × 3, where the columns overflow. Build the three layouts, checking each against the cards, then push them together starting with the units.Twenty-four units! Too many for one column — off to the bank.
6. 6 Exchange at the bank: twenty-four units become two ten-bars and four units. Continue up the columns, exchanging wherever a column holds ten or more.
7. 7 Read the product from the mat — 4,704 — stack the answer cards, and record the problem on paper.One thousand five hundred sixty-eight taken three times makes four thousand seven hundred four.
8. 8 In the virtual material, choose Multiplication. It asks for the same layout once per count — checking each time — then lets your child exchange and check the product place by place.

Points of interest

• Seeing three identical layouts side by side before the push-together
• Columns overflowing much more dramatically than in addition — sometimes two trades in one column
• The word "times" suddenly meaning something you can see

Control of error

• Each layout is checked against the cards before the next is built — a miscount shows up early
• A column holding ten or more cannot be read as a digit; the material demands the exchange
• The virtual Check confirms every place and the running total can be hidden until the child has an answer

Vocabulary

• multiplication
• times
• multiplicand
• multiplier
• product

Variations

• Skip-count the layouts before combining: 1,568… 3,136… 4,704 (with your help)
• Group multiplication: each family member builds one copy of the number, then all copies are combined

Extensions

• Write the problem vertically on paper and match each carried digit to a bank trade you actually made
• Compare with addition: work 1,568 + 1,568 + 1,568 on paper and ask which notation is quicker

Follow-up work (pencil & paper)

• Multiplication sheets with a one-digit multiplier — lay out the beads first, then solve the same problems in pencil.Printable: Multi-Digit Operations
• Place-value refreshers between sessions: reading and writing four-digit numbers keeps the columns automatic.Printable: Place Value & Expanded Form
• Same-addend hunt: your child writes each multiplication worked with beads as a long addition (1,568 + 1,568 + 1,568) and circles what repeats.

What comes next

Golden Bead Division completes the four operations: the child deals a large quantity fairly to skittles and meets sharing, remainders, and the reverse of multiplication.

Next in this strand: Golden Bead Division