Curriculum Connections

Counts Quantities 6-10

Students use the standard list of number words in order (six, seven, eight, nine, ten). They learn to count a set of objects by pairing each object with one and only one number. Students will understand when they count, they are thinking of what number is one greater and one less than another number.

Cardinality of a Group of Objects

Students are shown many different arrangements of objects. They will begin to understand that the total amount in a group is the same whether the objects are randomly arranged or counted in more organized ways such as using a five-frame or ten-frame.

Read and Write Numerals 6-10

Students read numerals 6 to 10 and write the numerals that tell how many objects are counted.

Equal Groups

Students compare groups of objects to tell whether they are equal in number or not equal in number. The focus is on comparing groups by matching objects one to one.

Greater Than and Less Than

Students continue to use a matching strategy to determine which of two groups is greater or lesser in number. Others might explain that one group is greater in number because it has a least one object left without a match. Students can use the matching strategy or a ten-frame to compare.

Comparing Numbers

Students count objects in two groups and write the numeral for each group. They are then asked to determine which number is greater and which is less. They begin to see that sets of objects can be compared by number, relating comparison to their knowledge of the counting sequence and not always using a group of objects.

Students will use apply what they have learned about counting to identify how many grapes each person grabbed and who grabbed more grapes.

Students solve "break apart" problems. They are given the starting amount and the amount that is taken away. Students use concrete representations and a subtraction equation to find the result. Students also solve "compare" problems. These situations involve a larger quantity, a smaller quantity and the difference between two quantities. Students are asked to find how many more or fewer in these problems. Use of Greg Tang's Six Step Problem Solving Process is helpful with these word problems.

Student will develop fluency with facts to 10 and use strategies to solve problems with sums up to 20.

ADDITION STRATEGIES:

Counting On: Students count 1, 2, or 3 from any number to add within 20. Number lines are used to illustrate this strategy.

Doubles and Near Doubles: Students learn to recognize doubles and near doubles when they add within 20.

Make a 10: Students use a ten-frame to help them complete addition facts with sums up to 20. Students will change one addend into a 10 to then have a 10 and some more to add.

Students will apply their understandings of addition strategies to figure out what spins the second game player spun.

Students will learn to add two-digit numbers within 100 using strategies that employ a hundred chart, an open number line, breaking numbers apart, and compensation. Students will also learn to solve one-step and two-step word problems involving addition and subtraction. These problems include "put together," "break apart," and "compare" situations. Bar diagrams and equations are used to represent the relationships between the quantities in the problems. Use of Greg Tang's Six Step Problem Solving Process is helpful with these word problems.

Students will develop computational fluency in addition within 100 using models and place-value strategies. Students will begin by using place-value blocks and drawings to find sums. It is helpful to remind students to organize their tens and ones into a ten-frame like arrangement when drawing to stay organized. Place-value blocks help develop an understanding of how to join the tens with the tens and the ones with the ones to find partial sums, and how to regroup when necessary. Students will also an understanding that the sum stays the same regardless of whether they add the tens first or ones first.

Students will apply their understandings of addition strategies and place value within 100 to determine how many stiles are piled up.

How can you use known multiplication facts to solve unknown facts? In this topic, students will use known facts and properties of multiplication to learn multiplication facts with factors of 3, 4, 6, 7, and 8.

How many bottles of water did the students drink? Students will apply what they know about multiplication to figure out how many bottles of water students drank while playing on the playground.

Note: 3-ACT Math is only in the odd-numbered topics.

How can you use known multiplication facts to find unknown division facts? In this topic, students will learn the inverse relationship between multiplication and division. Students will use multiplication facts to solve division without remainders. Students will also build on what they know about addition and subtraction fact families to apply fact families to multiplication and division.

How can you multiply by multiples of 10, 100, and 1,000? How can you multiply whole numbers? In this topic, students will use properties of multiplication and place-value understanding to multiply multiples of 10, 100, and 1,000 by 1-digit numbers.

How many stickers do you need to cover the box? Students will determine how many stickers it will take to cover the outside of a box. They will learn that it takes 19 stickers to cover one row on the longest side. Included in Act 2 are examples of student work with two very different answers, allowing students the chance to analyze others' ideas and whether or not the answers seem reasonable.

Note: 3-ACT math is only in the odd-numbered topics

How can you use a model to multiply? How can you use the Distributive Property to multiply? In this topic, students will use arrays, area models, the Distributive Property, and partial products to multiply two 2-digit numbers.

What are the standard procedures for estimating and finding products of multi-digit numbers? In this topic, students extend their understanding of multi-digit multiplication of whole numbers in preparation to moving to multiplication of decimals in the next topic.

How many seats are on the train? Students will apply what they know about multiplication to determine how many seats are in each passenger car and then determine how many seats are on the whole train.

Note: 3-ACT math is only in the odd-numbered topics.

What are some common procedures for estimating and finding products involving decimals? In this topic, students use different strategies to multiply both decimals and whole numbers and two decimals. Students also use estimation to determine if their answer is reasonable.