A Glance at a Sample Balanced Week in Junior Mathematics Grade 5 Patterning and Algebra, Number Sense and Numeration Constructing
Today:
Understanding
Through
Problem
Solving
Based on last week’s observations,
students appear ready for this
week’s learning goal: you can
multiply two-digit numbers by twodigit numbers using a variety of
strategies (e.g., friendly numbers,
distributive property).
Three-part lesson:
Activate prior knowledge with a
minds-on activity
e.g.,
• Examine student work from
yesterday
• Engage in a simplified version of
the main task
• Review key vocabulary and
terminology
• Review prior learning
Working on it:
Differentiate by selecting parallel
problems for students to work on in
pairs or alone.
e.g., (adapted from Gap Closing,
Multiplying and Dividing, Junior
Intermediate Student Book, page 15)
Lucy said that to figure out 19 × 8,
she starts by figuring out 20 × 8.
How will that help her figure out 19 ×
8?
OR
Lucy said that to figure out 39 × 88,
she starts by figuring out 40 × 88.
How will that help her figure out 39 ×
88?
Consolidate (large or small group)
and record key learnings: You can
use friendly numbers to help you find
products, you can break bigger
numbers into smaller numbers to
help you find products (distributive
property).
This is a glance at a sample week of instruction in a Mathematics classroom. It is intended to illustrate a Mathematics program that balances skills,
concepts, strategies and thinking processes. On any given day, teachers use professional judgment and creativity to make decisions in response to
students’ needs.
A balanced Mathematics program will look different in every classroom.
Today: Strengthening
Learning Through
Purposeful Practice Today: Building
Skills and
Competencies
Today: Strengthening
Learning Through
Purposeful
Practice
Today: Constructing
Understanding
Through Problem
Solving
Based on yesterday’s observations,
students would benefit from practice
with the distributive property.
Some students will work in a guided
group with the teacher while others
engage in purposeful practice in
pairs or independently.
Direct instruction/guided group:
e.g., use base ten blocks and
counters to model arrays. (Leaps
and Bounds 5/6, “Multiplying Whole
Numbers” pages 48 – 59)
Purposeful practice in pairs or
independently:
e.g., Students model the
multiplication sentences on page 19,
#2 in Gap Closing, Multiplying and
Dividing, Junior Intermediate
Student Book using base ten blocks
and apply the distributive property to
find the expanded number sentence.
Exit card: independent student
assessment for learning.
e.g., Joey knows that 40 x 60 =
2400, how does this help him
figure 42 x 60 = ___?
Based on yesterday’s
observations, students would
benefit from practice with the
skills of multiplication.
Working on it:
Differentiated centres that help
students build fluency with basic
facts.
e.g., “Multiplication Tic-Tac-Toe”
(Math Makes Sense Student
Book Grade 5, page 51), “The
Big Race” (Guide to Effective
Instruction in Mathematics K-6,
Grades 4-6, Volume 5, page 69),
building different arrays with the
same number of square tiles, etc.
While students are working in
centres, there is an opportunity
for individual conferencing and
support.
After differentiated centres,
students engage in individual
assessment of multiplication
facts.
e.g., Students record
multiplication sentences from an
independent game using cards or
dice. (Flip 2 cards or roll 2 dice
and write the number sentence.)
Based on yesterday’s observations,
students are ready to deepen their
understanding through another
problem. Students will begin by
working independently. They will
then join a partner to share thinking
and understanding.
Activate prior knowledge by
reflecting on this week’s learning
goal: you can multiply two-digit
numbers by two-digit numbers
using a variety of strategies (e.g.,
friendly numbers, distributive
property).
Working on it:
Select an appropriate question(s)
from the textbook, A Guide to
Effective Instruction in Mathematics
K-6 or another professional
resource that addresses the
expectations, learning goals and
students’ needs.
e.g., “29 students are going on a
field trip to a museum. The field trip
costs $20.00 per student. How
much will it cost for 29 students to
go on the field trip?” (A Guide to
Effective Instruction in Mathematics
K-6, Grades 4-6, Volume 3, page
48)
Looking at the strategies displayed
from consolidation, students reflect
and record their learning using a
math journal, think-pair-share, math
scrapbook, audio recording, etc.
e.g., “Which strategy, in your
opinion, is an efficient strategy?”
“How would you explain this
strategy to someone who has never
used it?”
(A Guide to Effective Instruction in
Mathematics K to 6, Grades 4-6,
Volume 3, page 52)
Large Group Consolidation:
highlight student solutions that show
the use of friendly numbers or the
distributive property.
e.g.,
• Gallery Walk: students use
stickies to label student work
that shows the use of friendly
numbers or examples of the
distributive property.
• Math Congress: students meet
in pairs to discuss how their
solutions are similar or different.
• Dotmocracy: students draw a
dot on any other paper that
shows the same multiplication
strategy that they selected.
Working on it:
Teacher differentiates learning
tasks based on individual student
needs in order to consolidate
understanding. Students might:
• Finish Centres
• Practice basic facts
• Apply strategies in a problemsolving context
Assessment of learning: individual
assessment and conferencing with
some students.
è There is evidence of
intention and balance
over time.
è There is a balance
between direct
instruction, collaborative
learning, and
independent practice.
è There is a balance
between problem based
learning, basic skills and
purposeful practice.
è There is a strong
connection between the
curriculum expectations
and the tasks.
è There is intentional use
of a variety of resources.
è All teacher choices are
intentional and
responsive to student
thinking and work.