Multiply and Regroup with Place Value Disks
Multiply and Regroup with Place Value Disks is a Grade 4 math skill that uses physical or drawn place value disks to model multi-digit multiplication by making regrouping (carrying) visible and concrete. When multiplying, for example, 3 x 214, students place disks for each digit and combine groups, regrouping 10 ones disks into 1 tens disk and 10 tens disks into 1 hundreds disk as needed. Taught in Chapter 11: Multiplication of up to 4 Digits by 1 Digit in Eureka Math Grade 4, this hands-on model bridges understanding from basic multiplication to the standard algorithm.
Key Concepts
To multiply a two digit number by a one digit number, calculate the partial products by multiplying the ones and tens places separately. If a place has 10 or more units, regroup them. The total product is the sum of the values in each place after regrouping. $$c \times (10a + b) = (c \times \text{ones}) + (c \times \text{tens})$$.
Common Questions
What are place value disks and how do they help with multiplication?
Place value disks are counters labeled with place values (1, 10, 100, 1000) used to model numbers concretely. In multiplication, you create multiple groups of disks and combine them, regrouping whenever a column accumulates 10 or more disks into the next higher unit.
How do you model 3 x 214 with place value disks?
Create 3 equal groups of 214 using disks: 3 groups of 2 hundred disks (600), 3 groups of 1 tens disk (30), and 3 groups of 4 one disks (12). Since 12 ones regroup to 1 ten and 2 ones, add the regrouped ten: 600 + 30 + 10 + 2 = 642.
How does regrouping in multiplication connect to the standard algorithm?
When the product in any place value column is 10 or more, the tens digit of that product is carried to the next column. Place value disks make this carrying visible — 10 ones disks physically become 1 tens disk, matching the carry in the algorithm.
Why do students use place value disks before learning the multiplication algorithm?
Place value disks make the meaning of regrouping concrete before students work abstractly with the algorithm. Seeing 10 ones become 1 ten physically helps students understand why they write a small carry digit above the next column in the standard procedure.
What grade introduces multi-digit multiplication with regrouping?
Multi-digit multiplication with regrouping is introduced in Grade 4, covered in Chapter 11 of Eureka Math Grade 4. Students multiply numbers with up to 4 digits by a single digit using concrete models, then the standard algorithm.
What chapter uses place value disks for multiplication in Eureka Math Grade 4?
Chapter 11: Multiplication of up to 4 Digits by 1 Digit in Eureka Math Grade 4 introduces multi-digit multiplication using place value disks and connects to the standard multiplication algorithm.