In this unit, students interpret and represent data
on scaled
picture graphs and scaled bar graphs. Then, they
learn the
concept of multiplication.
This is the first of four units that focus on
multiplication. In
this unit, students explore scaled picture graphs
and bar graphs
as an entry point for learning about equal-size
groups and
multiplication.
In grade 2, students analyzed picture graphs in which
one picture
represented one object and bar graphs that were
scaled by single
units. Here, students encounter picture graphs in
which each
picture represents more than one object and bar
graphs that were
scaled by 2 or 5 units. The idea that one picture
can represent
multiple objects helps to introduce the idea of
equal-size
groups.
Students learn that multiplication can mean finding
the total
number of objects in a groups of b objects each, and can be represented
by a×b . They then relate the idea of equal groups
and the
expression a×b to the rows and columns of an array. In
working
with arrays, students begin to notice the
commutative property
of multiplication.
In all cases, students make sense of the meaning of
multiplication expressions before finding their
value, and
before writing equations that relate two factors and
a product.
Later in the unit, students see situations in which
the total
number of objects is known but either the number of
groups or
the size of each group is not known. Problems with a
missing
factor offer students a preview to division.
Throughout the unit, provide access to connecting
cubes or
counters, as students may choose to use them to
represent and
solve problems.
Throughout the unit
Students work toward fluency in multiplying by 2, 5,
and 10. The
How Many Do You See routine is used to encourage
students to
look for equal groups. It prompts students to
subitize a group
of dots as one unit, see the iterations of the
groups, and
skip-count to say the total number of dots they see
in the
image. This routine progresses from dots to drawings
of equal
groups to array formations.
Here is a sampling of the How Many Do You See
warm-ups in the
unit.
| lesson 4 | lesson 18
|
|---|
 |  |
Number Talks are likewise designed to help students
build fluency
with equal groups and multiplication expressions.
The sequence
of expressions encourages students to relate
multiplication to
skip-counting. For example, in the
sequence 1×10 , 2×10 , 3×10 , 4×10 , students can discover that the products
increase in the
same way as in skip-counting by 10. Some Number
Talks elicit
students' understanding of addition and
subtraction within 100 in preparation for the
work in an upcoming unit.
Here is a sampling of the Number Talk warm-ups in the
unit.
| lesson 5 | lesson 15 | lesson 19 | lesson 20 |
|---|
2+2+2+2 2+2+2+2+2+2+2+2 5+5+5+5 5+5+5+5+5+5+5+5 | 1×10 2×10 3×10 4×10 | 10×2 9×2 8×2 7×2 | 70−10 68−10 70−12 68−12 |
