The total lunch bill for six people is $52. They add an $8 tip and
split the bill evenly. How much is each person’s equal share of
the total?
Make sense of problems and persevere in solving them.
Read the question carefully. Identify the hidden question you need to
answer to solve the problem. How much was the total bill after
adding the tip? ($60)
Grade 4
Luke collected 36 baseball cards and 34 football cards. Find the
number of cards in his collection without using a pencil and
paper.
Reason abstractly.
When students use mental math to add or subtract whole numbers,
they are reasoning abstractly.
Grade 4
A crayon company makes 17,491 green crayons and 15,063
red crayons. How many more green crayons are made than red
crayons?
A
B
C
D
2,428
3,463
10,456
32,554
Reason quantitatively.
Encourage students to estimate the answer before they solve the
problem.
Grade 4
Mr. Tran would like to buy a new sofa that costs $934. He can
pay the total all at once, or he can make a $125 payment each
month for 8 months. Which plan costs less? Explain.
Construct viable arguments and critique the reasoning of others.
Guide students to understand that they need to compare exact
amounts to solve this problem.
Grade 4
Find two ways to arrange 10 desks in equal rows. Then write
number sentences for each arrangement and describe how
these number sentences are similar.
Model with mathematics.
When students write multiplication sentences to describe an array,
they are modeling with mathematics.
Grade 4
One fifth-grade class has 11 boys and 11 girls. A second fifthgrade class has 10 boys and girls. There are 6 math teachers.
To find the total number of fifth-grade students, what
information us not needed?
A
B
C
D
The number of girls in the first class.
The number of boys in the first class.
The number of math teachers.
The number of boys in the second class.
Make sense of problems and persevere in solving them.
Remind students to eliminate wrong answers.
Grade 5
Which shows the Associative Property of Addition?
A
B
C
D
1.3 + 10 = 10 + 1.3
15.5 + 0 = 15.5
(3 + 10) + 7 = 3 + (10 + 7)
(3 + 10) + 7 = (10 + 3) + 7
Reason abstractly.
Remind students to eliminate wrong answers.
Grade 5
Suppose you want to buy software for your computer. One
piece of software costs $20.75. Another costs $10.59 and a
third costs $18.25. Use mental math to find the total cost.
Explain how much more is the first piece of software than the
second. Use mental math to decide.
Reason quantitatively.
Remind students that numbers can be rearranged and changed to
make exact calculations easy to do mentally.
Grade 5
Juan adds 3.8 + 4.6 and gets a sum of 84. Is his answer correct?
Tell how you know.
Construct viable arguments and critique the reasoning of others.
If students have difficulty understanding how Juan’s answer is not
correct, ask If you add two numbers less than 5, will their sum be
greater than 80?
Grade 5
Marcia has 27 red beads and 42 blue beads. How many beads
does she have in all? Write an equation and solve.
Model with mathematics.
Make sure students connect the problem to the visual model.
Grade 5
Look at the number patterns below. Write the missing numbers
then circle the number that tells how you counted to complete the
pattern.
8 10 12 ___
___
___
10
2
10 20 30 ___
___
___
5
10
Make sense of problems and persevere in solving them.
Students must make sense of the problem by first understanding what the
question is asking. Students must then persevere in solving the two part
questions by determining how to continue the pattern and then circling the
correct answer.
Kdg
Pick a number from 5-10. Write the number and use the ten-
frame to show the number you wrote.______________
Model with mathematics.
Students will apply their knowledge of numbers greater than 4 and one-toone correspondence by modeling how to make that number using the tenframe math tool.
Kdg
Gina has 7 stickers. She puts them on two cards. Show
different ways Gina can do this.
Make sense of problems and persevere in solving them.
Students must make sense of what the problem is asking and
persevere in being able to show the two different ways Gina made 7.
Grade 1
Write a subtraction sentence to solve for the model. Then
write two addition sentences.
7
*
*
*
*
*
*
*
Reason abstractly and quantitatively.
Students must use their reasoning skills to determine what
subtraction fact the part-part-total map shows and then by writing
the related addition facts.
Grade 1
Complete the picture to solve. Write the number sentences.
*
*
*
*
*
*
Marcy has some hair ribbons.
She has 6 pink ribbons.
The rest are purple ribbons.
She has 10 hair ribbons in all.
_____+ ______ = _________
_____+______ = _________
Construct viable arguments and critique the reasoning of others.
Students can listen or look at the picture and number sentences drawn to decide whether the problem
makes sense, matches the story problem and ask questions to help understand the other student completing
the problem.
Grade 1
Journal: Choose a two-digit number. Draw the number as
tens and ones. Then write the number in two different ways.
Model with mathematics.
Students must model their understanding of place value by selecting
the appropriate mat (tens and ones) to use, by drawing a rod of tens
and individual ones, and by writing the number in 2 different ways.
Grade 1
Make sense of problems and persevere in solving them.
Students will read and make sense of the problem to be able to
determine the answer.
Grade 2
Suppose you have 125 baseball cards. If you buy 100 more,
how many cards will you have?
Reason abstractly.
Children will be able to indentify that the tens or hundreds digit
changes when you increase or decrease a number by ten or a
hundred.
Grade 2
Raymond has 16 model planes that he wants to display. Will
he need more shelves if he puts 8 on a shelf or 4 on a shelf?
Explain.
Reason quantitatively.
Students need to think quantitatively to solve this problem. They
must understand what happens to the number of objects in each
group as the number of equal groups increase or decrease when the
total remains the same.
Grade 3
How can you create different polygons with different
attributes?
Construct viable arguments and critique the reasoning of others.
Consistently ask children to define shapes specifically by their
attributes, using examples and counter examples in their definitions.
Grade 2
A pan of cornbread is divided into 6 equal parts. Alana serves 2
of the parts. Is it reasonable to say she has served 2/6 of the
cornbread? Explain.
Construct viable arguments and critique the reasoning of others.
Students use the understanding of fractions to develop an argument
to support the reasonableness of their answer.
Grade 3
Robin bought a sheet of stickers. The stickers come in 5 rows
with 4 stickers in each row. Write a number sentence and draw
a picture to show the amount of stickers Robin bought.
___ + ___ + ___ + ___ + ___ = ___
Model with mathematics.
Students will use a number sentence and a drawing as a model to
help answer this question. The drawing will provide the students
with a concrete example of the word problem.
Grade 2